IMO, you overstate the issue of syntax. As a hobbyist in both programming and math, Coq's syntax has never been the reason I failed to complete a proof. But perhaps I'm just too dumb and my difficulties lie elsewhere, so that's just my 2c.
I think there's room for a spectrum of theorem provers made for academic pure mathematicians, industry programmers and everything in between. Those should perhaps not have identical syntax, neither should they have the same goals.
To support my point, here's an example of an exotic theorem prover: https://github.com/webyrd/mediKanren
It is aimed at medical researchers, and computes proofs about the medical literature, no less! This is a very different system and audience than which you are thinking about, but it's still a theorem prover.
I think there's room for a spectrum of theorem provers made for academic pure mathematicians, industry programmers and everything in between. Those should perhaps not have identical syntax, neither should they have the same goals.
To support my point, here's an example of an exotic theorem prover: https://github.com/webyrd/mediKanren It is aimed at medical researchers, and computes proofs about the medical literature, no less! This is a very different system and audience than which you are thinking about, but it's still a theorem prover.