Ive been considering this aswell. I think it wouldnt take much compute to host your account, or a couple if you invite friends to join. Its a website and a database after all. The bigger chunk of space consumed will be any images etc you share across instances, as they all go back to the home instance (your server) but images dont take much space.
Im still new to this as well, but this is what i think how it works. Let me know how you go!
Secure and privacy respecting DNS providers do exist. I use Quad9 on all my devices, including mobile. Adguard have DNS settings you can use that does everything you are wanting to do (secure, private, adblocking, malicious content blocker).
Theres also NextDNS if you wanted to throw them a couple bucks a month to do all the same thing. In theory, youd be doing the same thing that others are offering for free.
https://www.quad9.net/service/service-addresses-and-features
https://adguard-dns.io/en/public-dns.html
https://nextdns.io/
With nextDNS being US based, it might be subjected to information requests being apart of the 5 eyes.
But i digress, i think the hassle and maintenance of a VPS purely for DNS requests probably dont quite add up to the ease of using adguard or quad9. And its easy to change the DNS server on mobile (android at least, not sure on apple) in the connection settings, so you arent having to set up a tunnel specifically to rout your DNS requests.