So if you dont like the term mempool, how about unconfirmed transaction pool, as long as you know what Im talking about. I understand the transactions are not received at the same time by all nodes and miners, thats why I brought up as a requirement that the content of the next block has to be agreed upon early enough. And no, the blockchain still has its value since the content is only then secured with the proof-of-work requirement.
How do you have all nodes agree on the contents of the next block? Don't just say "somehow", provide exactly how you think they would be able to do this. Furthermore, this does in fact allow for the blockchain to be done away with. The Proof of Work is
how Bitcoin determines the transaction order and determines who is correct. Having some other method of determining the transaction order thus does not need the Bitcoin blockchain (note that this does not mean it can't use PoW or have PoW somewhere as part of it).
That's something to elaborate in more details, not because I didn't specify it that it means it is impossible. It is more about some consensus they could follow as an ordering rule. Rather than each miners having their own rule, if they all agreed on, it would give this benefit.
Here is a simple one I thought about, but eventually that could be improved to better account for low-fees transactions that haven't been included yet:
Transactions are ordered first by
transaction fees (satoshis/bytes) (highest to lowest)
then by
transaction size (lowest to highest)
then, as an additional filter, the destination addresses of each transaction are XORed together and the lowest (or highest).