Fully agree to your closing sentence. I thought the same - how nice would it be to target desktop and web via emscripten.
I had roughly 4 days for this 7drl challenge and eventually spent two days only for getting the build run via emscripten. Initially I used opengl 4.1 core but learned that I need to make it compatible with opengl 3.3 - so that it would run in webgl 2.0 which is similar to opengl es 3.0 in emscripten.
I needed to adjust all my glsl shaders and tackle some nasty bugs where things like the world generation would behave differently in the browser compared to the desktop version.
So I needed to check the random number generators and also convert the data structures from c-style arrays to std::vector.
Also the asset loading needed to be adjusted for the browser with preloading resources in the virtual filesystem.
All in all I'm quite happy with the results and that I was eventually still able to make a web build via emscripten, although I thought it would take way less time to get it to work. But it was time well invested - now I'm able to do cross-platform for desktop and web for future jams and next years 7drl!