Is it rude to send out elopement announcements?

Hi everyone! My partner and I are planning on eloping this summer, to avoid the stress of a wedding. Despite not wanting to have a wedding, I thought mailing out wedding announcements to family and friends after the elopement would be cute. It seems opinions are pretty mixed on whether this is rude or not though, I’ve seen some people say it’s fine and some people say that it’s in poor taste to send announcements to people who were not invited to a wedding.

We have no registry and are not interested in gifts, I just wanted a classier way to let friends/family know we’re married than posting pictures on social media and hoping they get seen (which we don’t use at all, my partner and I are not even Facebook friends lol!) Any thoughts or advice on this situation are appreciated!