I was reluctant to switch from Emby to Plex for this same reason but it turns out you can run plex self-hosted without any account. I have Plex running on a server and streaming from the Plex app on an LG TV without requiring an account.
I'll warn you that Plex will do everything possible to get you to add an account. One update (several years back) locked me out of making any changes to my server until I created an account.
