I'm not interested in talking about all that, much of it is still speculation and there are plenty of articles being written about the moral issues, some from Mt Pious and others from more humble locales. All of the opinion takes are fairly obvious and each will likely say more about the author than the actual situation.
To me the much more interesting thought is what Baylor will do with their head coaching vacancy if they have to dismiss Briles for some level of moral failure.
Assumption 1: They can't go back to the Briles tree
It stings for Baylor, but it's true. You can't maintain most of the same staff and go back to this well and then pretend like you've really addressed the issues, even if Phil Montgomery or Dino Babers can be completely trusted to run programs with the utmost integrity.
If things at Baylor are bad enough that Briles would have to go then the next hire has to take a lot of optics into account. Hurrying up the Briles succession plan and handing the kingdom to one of his assistants will NOT satiate the public cries for justice.
Assumption 2: They need to stick with the spread
It's hard to win in the Big 12, especially at a smaller Texas program, if you aren't going to capitalize on the state's knack for producing great players who've been raised up in the spread.
The powerhouse high school programs across the state are known for using the middle school feeders to train all of their players in the same system. By the time the players are upperclassmen in high school they deeply understand the system and the techniques and are consequently much better than players new to the deal.
It's like the Spartiate class of elites in ancient Greece who grew up trained for hoplite warfare going up against the tradesmen/peasant-hoplite armies of their city-state rivals. This is a huge advantage to pass on unless you know you can get the right fits for your non-spread system and you are dang good at teaching it.
All that to say, there are major advantages to be had from running the spread offense when your base of talent is Texas high schoolers. If you install any other system you're basically running uphill, to say nothing of then struggling to make the most of the currently assembled talent.
Assumption 3: A new coach would be working at a disadvantage
If Baylor feels like they have to remove Briles as part of an attempt to clean up the program then you can count on the new coach having little to no leeway in terms of the players he can bring in or the behavior he can tolerate.
Also he'll be replacing a legend who is almost single-handedly responsible for the greatest run in Baylor football history and is one of the most brilliant offensive coaches in the history of the game.
That's a tough job. You want to be the guy who replaces the guy who replaces THE GUY. If Baylor has to replace Briles I think they'll have a tougher job bringing in coaching talent than one might assume given the momentum Briles has built up with recruiting and a new stadium.
The next hire would essentially be a caretaker both of the house Briles built AND the attempt to clean up the image. Tough gig, very political situation. A win here would be hiring someone who can keep the program from burning to the ground while the program regroups.
Suggestion 1: Hire a defensive coach
It'd need to be someone with a proven track record of defensing spread offenses and ideally either someone who was a defensive head coach who hired spread OCs or a DC who worked alongside spread O coaches.
Why? Because for the reasons I mention above it's not rocket science to build an effective spread offense at a Texas program with the resources of Baylor. Any half-decent spread O college coach should be able to field a solid offense with what Briles would theoretically be leaving behind and what the Bears could expect to bring aboard in the future.
With Art at the helm Baylor could count on running the best spread offense in the conference, if he's gone they should try to find another angle where they can be at advantage because that one is gone. For instance, being the team that has as good an offense as most anyone else but can also play defense. That's a nice niche to try and fill and Baylor's most successful teams under Briles have been the ones that could play a little defense.
Defensive coaches are also often known for building a tough, disciplined culture and Baylor could sure benefit from a bunch of spring narratives (I'd assume they'd go interim in 2016 and make a hire for 2017) about increased accountability, toughness, and "now we play defense" quotes.
Suggestion 2: Stick with the 3-4 defense
There's an advantage to be had by playing a style of defense that's somewhat unique and, as Art is now finding, it's much easier to find pieces up front to staff a 3-4 squad than to run a 4-3 that's dependent on good pass-rushing DEs. Granted TCU and K-State find a way, and if you can hire a coach that's great at developing 4-3 DL then go for it, but the 3-4 makes for an easier path to moving players around and thwarting spread Os.
If Briles is removed it'll be partly due to the sins of players he brought aboard out of an attempt to find the elusive defensive superstar. His system could always be counted on to create superstars on offense but on defense they had too little margin.
Some names that are probably unlikely but you'll hear mentioned anyways
Chad Morris and Tom Herman aren't walking through that door. Both of them have eyes on the bigger prizes, Texas and A&M, and Herman has a good shot at landing another top 10 gig if Strong manages to survive in Austin. Morris is currently at about the level that Baylor could expect to hire from and is struggling through the fact that he inherited a tough situation, he walked out at Clemson RIGHT before Deshaun Watson was ready to dominate, and there are other up and coming coaches within his own conference.
However, there's a chance A&M falls apart this year and Chad Morris would certainly be in contention for that gig. Either way, if he's willing to be patient he can probably do better than having to replace Briles in a sticky situation at Baylor.
If the Bears can get him, they should.
Some names to consider...
I'm not going to abide by both of my above suggestions about the defense here I just wanted to throw those out there as possible advantages for Baylor to explore.
Bob Stitt, Montana
It's only a matter of time, right? Stitt is one of the most clever Air Raid coaches around and he's been running the offense at schools that don't have access to anywhere near the level of talent that is common to Baylor. He's used to working with players that you wouldn't worry about coming with a rap sheet. He also had a pretty solid defense this year at Montana (a 4-2-5) and just might be a guy capable of also overseeing a strong unit on that side of the ball.
Doug Meacham/Sonny Cumbie
Two more very good Air Raid coaches, plus you'd deal a damaging blow to Gary Patterson and that would be at least bittersweet, right? I don't know if either would come or not but it seems reasonable to at least go for it.
David Bailiff, Rice
Bailiff runs a physical brand of spread combined with a Patterson-esque 4-2-5 defense and he does it all with players that have to be able to get into Rice. I don't know what a Bailiff-Baylor program's ceiling is, probably higher than you might guess, but he'd be the perfect optics hire and at 57 perhaps he can just play the role of caretaker for a reasonable period of time before retiring. Then you make a splashier hire.
Todd Orlando, Houston
It'd be nice to see what he does with the Cougar defense now that they won't have an NFL cornerback anchoring things (unless they have another of those on the roster now that Will Jackson's gone) but Orlando has a pretty nice track record of building great defenses from parts of the sort that are definitely accessible at Baylor.
Willie Fritz, Tulane
This suggestion came from @BearsTruthS11, a 247 writer for the Baylor site.
Fritz is a defensive minded guy who's had success at multiple stops, including Sam Houston State. When Tom Herman was looking for an OL coach to bring physicality to his smashmouth spread at Houston he went to SH St to poach their assistant. I haven't watched his teams play but he checks most all my boxes.
There are probably some really solid D2 options out there that I'd explore were I put in charge of this process, I'd also look to pillage the Texas HS ranks for some assistants were I the new head man. Especially if I came from a non-Texas background.
Anyways perhaps this is all just a mental exercise and Briles will be exonerated or otherwise protected and the Bear machine can keep chugging along. If not, those are some of the factors that I'd look at in evaluating the hire.