If that’s a concern, Teamviewer has the option to connect over the LAN instead of route through their servers. I’ve never used anydesk, so can’t speak to that. In my case, I have a high end desktop in my basement that I remote into from my laptop when I’m home. That way I can still spend time with the wife and kids and not be relegated to the basement office by myself. I just use the local address instead of routing through Teamviewer’s servers. If I’m not home, I connect in through my VPN and then use the local address.