I shall try again to phrase it differently and shorter:
If I search for browser games on a hoster, I want to find browser games on that hoster and not browser games that are hosted somewhere.
The situation is different if I search on a generic game searching site. Itch is not the google for indie games.
That’s fine. If this suggestion is implemented, there should be a clear indication if the project is available via a third party and not directly on itch. So you can avoid such projects if they are not your cup of tea.
And there can be extra guardrails too, like your project must be otherwise present on the platform. So itch doesn’t turn into an ad board for 3rd party services. Though I think it’s a bit premature to worry about that. And, besides, that can already take place regardless of this suggestion, as you are not required to upload any files for your project.
I do not think it premature to discuss the benefits, ramifications, obstacles, and other things related to a feature suggestion. That is what discussions are for. There is a feature request button for "silent" suggestions.
Maybe someone will speak up and gives insight why this would be an excellent addition to Itch. You already heard two voices that basically said, they want to find projects on Itch when searching on Itch.
There even is precedent for part of the thematic in your suggestion. External file hosters. Those can't be filtered too. So when they would add a filter option for hosted on Itch/hosted external this might be applied to browser games too.
