If that existed, would it be possible to streamline the process such that people could just click a link and immediately get a client configured to publish to that relay and the relay automatically knew who that person was?
What about a relay with an "invitation" system to welcome new users without asking them to pay upfront? https://lobste.rs/about#invitations
Discussion
Not pay up front means pay later? I don't see how nostr works without paid relays. If users don't pay, eventually they will need ads and other revenue streams or they will be unsustainable.
Reddit-like community solutions could also be envisioned, where you can join a relay and read/like/boost but not write unless you wait x days (anti spam) or pay a quick access fee.
At least people have access to quality content and load speeds from the get go, which helps attract new people. Paid 'members' could also have additional privileges in that specific client/relay
you'd need buy in from the clients unless the relay runs its own fork