Is this a translation issue? There are several things you say that make me believe there are things lost in translation. I shall try to exchange the generic you with one in this post, as that might have lead to misunderstandings.
You assumed something that was never stated and wasn’t the point of the suggestion.
I am not sure to what you are referring to, because I did not make any assumptions in such a way. And reading further, I am rather sure I understood your feature suggestion quite well.
Your suggestion is to make projects discoverable in the Play in browser section, even when they do not have a web-playable thingy actually on Itch, but by giving ability to state that the game is hosted elsewhere. Is this not so?
I posed two scenarios, where one would either have no downloadable files or one would have some. And gave my opinion and reasoning for having that opinion for both cases.
But you don’t need to download it and host it yourself, locally or otherwise. I simply mention that you can also download the sources for self-hosting, if you want to.
That makes little sense. What exactly do you mean by "host it yourself/self-hosting"? The second part would imply redistribution. The normal use case seen on other projects would be to open the index.html file on one's hard drive with a browser - and that would not be called hosting, hence my confusion.
Safari
So let me get this straight: your web project would not properly run on Itch when accessing it with Safari. But uploading it to Itch anways for all the people not using Safari was not an option? You could check for browser when starting the app and redirect people to your homepage and explaining that it does not work in that combination (Itch+this project+safari). And also put that in the description.
Well, when I try to run certain browser games on my phone, I just get the message that this and that will not run. Bad luck. Not all browser things run on all browsers. There are even flash games still on Itch and those will not run on most browsers, not only not on Safari. https://itch.io/games/flash/platform-web
The project is available in the browser, but not directly on itch, for technical reasons. Still, users might be interested in it and the fact that it runs in a browser, even if you cannot do it directly on itch.
If one makes a game, a game for Windows in this example, that also has a version for Linux, would you want to have that game appear in the section that officially proclaims that the game runs on a platform, even though the version for that platform is not actually on Itch? Like, one would only have the Linux version on github or whatever.