Who said anything about the project not being downloadable on itch? It is downloadable, for every desktop platform, and even the web version is available for download (for self-hosting), if you so choose. But the web version requires a server configuration not possible on itch (and probably for a good reason), and there are also other usability concerns with running it embedded.
This cannot be solved by a demo, as it’s not about features. And as I mentioned, the description already points users to the web version, if that’s interesting to them. The issue is that the project is not discoverable if the user looks for this type of project with a browser support.
Having an explicit option for browser-compatible versions which are hosted elsewhere can be used to gracefully handle user concerns, actually. Itch can have an explicit message that the project is hosted by a third party and even link some FAQ that explains the risks. Ultimately, it wouldn’t be any different from a link in a description, just with a benefit of actually being discoverable by users.
If that’s still suspicious to you, that’s fine. I just don’t see this as an argument against helping developers and users looking for browser apps and games to connect.