Yeah, that's true to an extent, but it's not like a new AD is going to just waltz in on his first day and can a guy who's doing his job well. For starters, there's a lot more to being an AD than just overseeing football. Secondly, the football coach is going to have a buyout in place, right? So that provides a barrier to willy-nilly termination. Plus, a new AD isn't going to want to have to commit to said buyout if he doesn't have to, for the sheer fact it's going to be a lot of money. No self-respecting AD is going to want to ask his bosses for an extra $5M $8M in the budget in year 1 to fire a guy doing a good job simply because he doesn't feel the coach shares the same "synergy". If that were to happen, that might be a signal to me that the AD hire was wrong, not the coaching hire.
Where I see your scenario coming into play more is at the time when a renewal is up for grabs a few years in. At a more realistic time where the AD would have a choice to make. I can appreciate that there is some risk for the new coach down the line, say years 3-5 somewhere. But when you consider a 4x pay bump, the fact that you have a contract that can't be terminated without a buyout, coupled with the fact that a good boss shouldn't want to fire you if you're doing your job well... I think those things more than mitigate the risk we're talking about for the coach. But that's just me.