Some minuscule portion of individual users may do so.
Organizations will implement eurodns as best practice for regulatory compliance. Providers will do so as well.
Almost every internet device uses whatever dhcp gives them as dns. When all the companies, government bodies and providers use eurodns to be compliant with the regulatory frameworks that allow them to continue operating in the eu that change will trickle down to users automatically.
It’s also worth remembering that surveillance is extremely normalized in the eu and eurozone compared to many other nations and areas. Of the vanishingly small percentage of users who are both aware of the concept of dns and choose to change it, a portion of them will accept and use eurodns.
Again, you may think I’m wrong but give it a few years.
You can’t use the cell network and preserve your anonymity without committing identity theft or fraud crimes or without someone else willingly laundering sims with you.
It’s almost always better to treat your phone and cell network usage as not anonymous unless you only need to do a few specific things.