Not sure if the model-checking communities would agree with you there. For example CTL-star [0] mixes tree-logic and linear-temporal, then PCTL adds probability on top. Knowledge, belief, and strategy-logics are also mixed pretty freely in at least some model checkers. Using mixed combinations of different-flavored logic does seem to be going OK in practice, but I guess this works best when those diverse logics can all be reduced towards the same primitive data structures that you want to actually crunch (like binary decision diagrams, or whatever).
If no primitive/fast/generic structure can really be shared between logics, then you may be stuck with some irreconcilable continuous-vs-discrete or deterministic-vs-probabilistic disconnect, and then require multiple model-checkers for different pieces of one problem. So even if mixing different flavors of logics is already routine.. there's lots of improvements to hope for if practically everything can be directly represented in one place like lean. Just like mathematicians don't worry much about switching back and forth from geometry/algebra, less friction between representations would be great.
Speaking of CTL, shout out to Emerson[1], who won a Turing award. If he hadn't died recently, I think he'd be surprised to hear anyone suggest he was a philosopher instead of a computer scientist ;)
[0]: https://en.wikipedia.org/wiki/CTL* [1]: https://en.wikipedia.org/wiki/E._Allen_Emerson