Yes, the Proxium relay is doing this: https://github.com/dezh-tech/ddsr/tree/main/proxium
Soon we will run an instance for nostr:nprofile1qqst72lw22q3f8rux5846y4wxt63f3uxflcsspgc9aqhs5uv93ppqpcpz4mhxue69uhk5etvd3ukv6tndqhxcctwvshszrnhwden5te0dehhxtnvdakz7qghwaehxw309aex2mrp0yh8qunfd4skctnwv46z7rsvwnd and users will have access to it too without any additional configuration or payments.
It broadcasts your note to all other relays and fetches notes from all other relays.
You can even publish a list of relays you want the proxium to read or write to.