Well, I'd argue that's more an issue of the web application. If you're on a system with limited resources, and the webapp insists on opening hundreds of connections, assuming they're free of charge, it's a bit silly.
Anyway, this is unlikely to change anytime soon, given the Postgres connection/process model. We're continuously improving things, but each connection has some non-negligible costs (CPU, memory), so in those cases a connection pool is still a good idea.
Several thousands are - at least up until now. V14 will improve this substantially.