With regards to BGFX, the author has added an option to set max frame latency, in the same way we do it in D3D9ex. As far as I know, baseline MAME is not benefiting from this feature yet, but it'd be trivial to add it.
The main concern for us with BGFX is that it doesn't support full screen exclusive rendering. Its documentation says "not implemented yet". Based on the web the feature has been requested to the author a few times already. He probably has other priorities, that's understandable. Probably he expects full screen exclusive mode will be deprecated anyway in a near future, so if he postpones it long enough it will become unnecessary.
My previous "implementation" of fullscreen exclusive mode through BGFX was a hack around the D3D11 backend, which obviously got broken as soon as the author made a serious rework of his code. Now after thinking of it, I believe it's a bad idea to even try again.
The main problem, imho, is that the interface itself of bgfx initialization only takes width and height, while targeting video modes accurately requires at least width, height and refresh (3 params), I say at least because it's desirable to also take interlace as a param. This oversimplification of the video phenomenon is an issue with most emulators, by the way, and the reason behind most compatibility problems with custom video modes, due to emulator authors' indifference or plain ignorance about video nature.
Having to add more params to the interface involves bulk changes all through the api. This could only be done in a clean, consistent way, by the author himself. For me, even figuring out what that code does is very difficult. It's written by a genius, but he didn't write it for others to understand.
With regards to GroovyMAME, not having support through BGFX seriously limits the viability of the project in the future. It might lead to a final project stall, or maybe an unlikely scenario where there's a completely separate backend for CRTs without any fancy shaders or anything (a major and unlikely to happen undertaking), and BFGX (hopefully with proper latency) for everyone else.