I understand that a pruned node needs to download all the blockchain in order to verify the blocks and construct the UTXO set.
But wouldn't be possible to download the headers only?
Let's say if the current block is 100 we download 100 headers and we consider the 94 first headers as valid. (100-6 = 94 , 6 is arbitrary and can be changed to prevent reorg) We download blocks 88 to 94 and consider their data as valid. And when receiving a transaction we check if this transaction is included in the blocks considered as valid.
And we constantly update that when a new header is added to the header chain. If the server is down then it won't notice the payment but that's another problem.
Can it work to receive payments ? I understand that as long as we never construct the UTXO set we can't create transactions and can't verify blocks. But does this idea of trusting proof of work only can work to receive payments?
or am I missing something ?