Was using AnyDesk (until it went to shit), then Teamviewer (before they went to shit) and a ton of other VNC and remote desktop options, but did finally land on self-hosting RustDesk.
It's been VERY solid and reliable for me, but what you just brought up concerns me.
I checked my filter log (from Adguard on Windows) to see if Rustdesk is calling home, and I'm not seeing anything after multiple connections and several hours of use. I guess these things aren't a concern with the self-hosted deployment?