No one claims, it is impossible to do. And a single filter was implemented in a day or so.
The problem is not the filtering logic itself, imho. That external site would break down, if it would receive the traffic Itch receives. You do not know the server load a search query causes and you do not know the difference in server load a negated search query causes in comparison. That you need to be logged in to be allowed to use the single exclude query, speaks volumes to me.
Itch's system under the hood is obviously optimimsed for overlapping positive filters. You can't simply overlap a negated filter with the same system. Not if you build nightly lists of those things, to prepare for the querys. They would probably have to build a (all-x) filter for all tags. And there are tags that have like 5 items. They did this for the no-ai tag.
You know what breaks down first, when Itch suffers yet another ddos attack? Browse filters with several tags.
I can simulate multiple tag exclusion on Itch. Client side. Takes a few minutes to set up, depending on the tags, and works flawless. But it does me no good. It's useless to reduce the clutter on the front pages. Oh, trivially, we could remove most games on page 1+2 with 2-3 negative tags. But is that what we need and want? Do we really want to look at "popular" games without a tag preference, but remove the actual popular games? There are far too many games for that. And the tags are just not good for negative filtering anyway.
Most people seem to care for the top pages, and what we need there is not a tag filter. It is an hide-this button. With filters you will visit next week again and the same clutter that was not cought in your filters will still be there. Plus you will filter away games that you might not have wanted to filter away.