Unfortunately for users, there are a lot of complex policies that different relays adopt which make them unsuitable for inbox/outbox usage.

If a relay requires payment to write, and you use it as your outbox without paying, then your messages will not be accepted by that relay.

If a relay requires payment to read, and you use it as your outbox (paying or not), then most users can't read your posts because they didn't sign up for that same relay.

If a relay requires AUTH to defeat spam, and you use it as your INBOX, then people who care about privacy will not reply to your messages.

I could go on, the list of gotchas is far longer than just this.

Gossip client, admittedly written for technical people not normies, has a "test relay" button to check if a relay is suitable as an outbox or inbox.