In any case, if you want to filter your traffic when you're away (be it with a network ad blocker or a proxy server) you will need to have a way to connect to said server.

Local browser extensions only detect what has been shipped to the browser by the web server, which is why they work at home or on mobile data, all the processing is done locally on the device.

A filtering DNS server, or a proxy server, will position itself between the web server you're trying to join and your device, and take out the ads and tracking. But to be able to use that server, it needs to be on the same network as your device. It's all good when you're at home, but when you're away, suddenly you two are separate. Hence the need for a VPN to connect your phone back to your home network.

You could make it public facing, but that's pretty much the worst thing you could do, security-wise. There are so many automated threats that actively try every waking minute of the day to get into an insecure home network to find of value, or to lay a time bomb that will allow them to do more, that you don't want to mess with that. For real. Don't mess with public-facing services.