If you using some central authority to say who is a valid node and who isn't, which you would need for mobile phone numbers, then why bother with trying to decentralize at all? That same central authority can verify transaction are valid. No need for any of this peer validation stuff.
A central authority like that is possible, but I think it would be very hard to get something like that off the ground, in that the government would eventually shutdown whoever was processing mobile phone numbers. Even Facebook is having trouble getting their (centralized) Libra coin signed off by the various governments, and that is a half a trillion dollar company.
The inner-inner paper (the one referenced by the paper referenced by the paper) gets around this problem using a social network, where you have a neighbor Fred that you met in person, who has a Butcher Dave, and so on. This doesn't seem easy as well. PGP email encryption had the same sort of web of trust idea. There are even "signing" parties where a bunch of people get together to verify each others identity. But still, not many people have a PGP key, much less have it verified by the PGP web of trust: https://en.wikipedia.org/wiki/Key_signing_party
> PPS: the real cost of a Bitcoin node could also be considered the cost to operate it, that is to write a block, and that in turn is costly, which presents the problem and its solution in an elegant unified way.
Well, a node isn't necessarily a miner, and most aren't, actually. One purpose of a node that isn't a miner is to send out transactions on behalf of an individual owner of bitcoin onto the network. Also, a block explorer website would have one to query the blockchain and extract the information to be displayed on its site, and of course an exchange would need a node to perform deposits and withdrawals. Nodes don't have to write blocks, only receive and validate them, and a sybil attacker just needs to create nodes that pretend to validate, it doesn't have to care about having an accurate view of the blockchain. This is very cheap.