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.