I don't know how to articulate the uncomfortable feeling I'd be having, about something 'inside' the database doing the download and making requests to other systems outside a boundary. It might be a security threat or just my inexperience, how common is it for postgres extensions to do this?
I feel the same way. I think it's useful to think of a database as simply a fast storage and lookup for data. When it starts to run network code or run doom it breaks our expectations. This will confuse people on your team, and confusion creates security problems and tech debt.
It's cool that postgresql can do this, and I've even bookmarked the project. But in my projects I expect all network code and API access like this to be on the same application layer.