You're correct. WebGL does require extra validation compared to native GL, but it's effectively the same API as OpenGL ES 2.0/3.0 and Emscripten handles the translation from C/C++ for you.
There's some overhead but it's negligible (assuming you're not making overly redundant API calls.)
And that last part is key: for modern high-performance graphics acceleration, the name of the game is "maximum throughput with minimum API interactions."
If your data isn't structured for fast rendering, it doesn't matter much what language you're using; they'll all be too slow.
There's some overhead but it's negligible (assuming you're not making overly redundant API calls.)