While we will most likely offer a web UI for extension installation at some point, I don't think it will help for the situation you describe.
The most common approach by the Flarum hosting services that exist at this point is I believe a single codebase that's used by all forums, so you can't have individual forums install additional extensions that other forums don't have. So even if we do introduce a web UI for extension (un)installation, I'm certain most of the cheapest Flarum hosting services will have to disable it anyway and provide you with a fixed list of extensions. Only hosting services that provide you with a dedicated instance would likely offer this feature, and they likely won't be cheaper than hosting yourself on a VPS.