They do but they never got something as good, it's multiple megabytes for a single empty scene with a long initialization time and doesn't run as well as it should (especially on mobile) when you consider old flash games were running on old pentium could be just a few kb and started instantly (and were 1 single streamable file).

If you are only targeting the web, you're better off with a game engine specific to the web.

Epic already abandoned the Emscripten toolchain sadly.