Speaking as someone with experience with many of those things (PL theory/formal verification background), I don't think they're even close to being a silver bullet.
Coming up with the right abstractions and the right domain model is difficult (especially if you just sit down and try to come up with stuff, you're likely to get it wrong the first time around). Knowing about some of those things could help you come up with better abstractions, but it's neither necessary nor sufficient to ensure that you will.
Take dependent types for example. They allow you to express more program invariants or correctness properties in your types. But actually using them requires you to write proofs (at least, if you're using them to their full potential). And I do think that in general System F like type systems hit a nice sweet spot and are generally good enough for the stuff that you might actually want to handle on the type system level.
I've also run into similar "proof-like" situations with much simpler type systems like those of Haskell and Rust, where I was structuring my types to "make illegal states unrepresentable", but in the process ended up complicating my program due to having to match the structure of my program to the expected structure of the types. Sometimes it is nice to _not_ to have the type system enforce some of your invariants. (Such things are also doable with dependent types of course, but this is just an example of some of the tradeoffs involved).
You can also still have a shitty domain model even if you use all of those fancy tools. They just allow you to be very formal/precise about the domain model (and do perhaps encourage some more uniformity by making it more annoying to express ugly or complicated things).