That's not a very good prime directive.
Don't regulate things that don't need to be regulated, i.e. unless there is a very material benefit from it.
If the EU is concerned about WW3 level resiliency for these services, they can accomplish that themselves with a few cord, 'hardened' services that meet their criteria. For 'regular operations' it seems we're going quite well right now.
Unless there is a threat posed by these heretofore independent operators ... then I'm don't see any obvious material benefit here.
I'm wondering if somehow these entities could be compromised in a way that makes them a problem, more so than just 'going offline', in which case, maybe there are some benefits.
There is a simpler solution rather than enforcing EU oversight over root DNSes.
It doesn't seem arbitrary to me. The service provided exists in many EU countries, and therefore must eventually be harmonised. This is the prime directive of the project.