Who guarantees the integrity? A central authority? The existing community?
What if a new member decided to join the community, he'd have to trust either the central authority or the "old" community (the community members that once had access to the full blockchain before it was pruned). Doesn't sound like something i'd want to be part of.
It's guaranteed by blockchain itself. You can not add or replace anything in the existing blocks so you can be sure that "this unspent output" is valid since the block which contains this transaction does not break blockchain integrity
It's true that currently, you cannot change anything in a block because it's a blockchain. The header of the next block contains the hash of the header of the previous block, the merkle tree of the transactions, a nonce and some other data that isn't interesting in this discussion.
So, pruning leads to this situation for a newcomer (unless i'm missing somehting here):
Block height x header: version,
hash of header of block x-1 that cannot be verified, merkle root, time, nbits, nonce
Block height x+1 header: version, hash of header of block x, merkle root, time, nbits, nonce
Block height x+2 header: version, hash of header of block x+1, merkle root, time, nbits, nonce
It's the very first line that's interesting: nobody can verify that the hash of the header of block (height x-1) is correct, because we collectively pruned that block if we'd followed your proposal. Sure, people that were here since the beginning should have no problem with this, they once stored block height x-1, so there would be no reason not to trust block height x's header...
But if a newcomer would enter the community, he'd just have to assume that block height x's header is valid, but he'd have no way to independently verify this.
This would also mean he'd have no way of knowing his UTXO was built correctly, unless somebody was sending him all historic blocks, which cannot be done if they were collectively replaced by empty placeholders like you proposed.
Now, bitcoin core already allows you to prune your blockchain locally, and as long as some people still store the complete blockchain, everything is fine IMHO. You can even switch to an SPV wallet if you don't want to sync, but the moment everybody prunes the first couple of blocks, new members would have to start trusting other members instead of being able to verify everything themselfs. This might still be fine in the beginning (eventough i think it's not fine), but in the end we'd have to start trusting a decreasing number of people that once stored the very first blocks, centralising the trust to these individuals.
Sure, it's a moving chain, and as long as you were there from the start you can prune whatever you want and still trust the whole system... It's just that if you were not there from the start, and you only trust yourself (like you should do), you're starting to see the problems.