I think you have that backwards. How can you create the UTXO if you don't have a full copy of the chain?
How many full nodes with the full copy of the distributed chain do you think is necessary to maintain both a fair distribution level and redundancy for security?
I don't think it can ensure that. All the nodes storing a certain block could disappear from the network at the same time. Where's the full copy now?
Either we could have enough redundancy with DHT to make this probabilistically impossible, or have enough archival full historical nodes. I would suggest both.
Currently, we have only ~6,400 full nodes active. I believe this number is too low and I assume you do as well. What is the bare minimum of nodes that would make you feel comfortable? Is it a set amount given enough distribution worldwide? Is there a certain ratio of bitcoin users to full node maintainers that makes you feel comfortable?