plus_id : {a} (fin a) => [a] -> Bit
plus_id x = x + 0 == x
You'd first have to instantiate `a` to some concrete size, rather than proving it for all `a`, which would be a beginner-level proof in Coq or Agda: Main> :prove plus_id
Not a monomorphic type:
{a} (fin a) => [a] -> Bit
Main> :prove plus_id : [32] -> Bit
Q.E.D.
So overall I'd say it's the classic story of the tradeoffs of a DSL. It's easier to get up, running, and proving things within the domain, but the domain itself is more restricted.
Another reason is simply productivity. Since the DSL is hosted within Haskell, we get the benefit of a fully-featured, expressive language for metaprogramming and abstraction of Ivory/Tower code. This has been crucial for letting us produce a functional autopilot (and board-support package/drivers) in only ~4 engineer-years.
We also have a stand-alone concrete syntax for Ivory that is intended to be more familiar to C/C++ programmers. It's being used heavily by our partners at Boeing on their Unmanned Little Bird. While they aren't reaping as many of the abstraction benefits as users of the EDSL, the fact that they can mostly focus on writing type-correct code vs. figuring out correct annotations makes them quite productive still.