Apps are not manuall added or tested to the Itch app repository. It just is a dedicated browser with some extras to access the normal Itch website. And those games on the site are also not added by Itch staff. They are added by the publishers. Often amateurs. And with a gazillion different ways of distribution. Including file hosters.
tl;dr Not all games are compatible with the Itch app.
And I do not think it is conceptually a general purpose game launcher, as you cannot add third party games. And even if it is from the Itch website, you would need ability to add 3rd party games to add games, even if you downloaded them from Itch.