A caveat at the outset: I am only in DI. IMO, the #1 thing they need to fix -- even more than EEs -- is the recruiting penalty a new coach faces when taking over a program. It is extremely difficult to come into a new program (whether or not you're taking over for a human coach) and have even a chance of session 2 recruiting success (leaving aside the "long-term coach" preference goes away for 10 or so seasons). It doesn't incentivize movement and strongly incentivizes mid-majors to stay where they are, especially since conference cash has been taken away. But more importantly, I'm not sure why it's a good business decision to punish successful coaches, who presumably are the folks who have spent time/money to rise to the top of DI. The problem, though, is that I've spent some time thinking about this, and I'm not sure there's a quick/easy fix that also retains at least a modicum of realism (aside from there being no signings the first couple of periods in session 2, which I am disappointed that WIS hasn't already implemented). Maybe make player actions easier to unlock for new coaches? Maybe add a "coach prestige" preference -- so if you're a winner at the mid-major level, you have more credibility with recruits? I don't know.
In light of this, I'm not sure firings need to be a priority -- from what I'm seeing right now in DI, elite programs are open and available (some big 6 conferences are less than 50% full).