When we can agree on mempool sorting order, we can just confirm first n-transactions that are at least 10 mins old. What's missing? When we can agree on a mempool sorting order, we can just confirm first n-transactions (or 80% of transactions) that are at least 10 minutes old.  Then, we can transfer (broadcast) the block header and a hash to the set of all confirmed transactions.

Just consider this as an aggressive version of BIP152, compact blocks.

This kind of method will work for transactions of any size; both confirming 10 transactions and 1 million transactions are the same.

What's missing? Why are we not doing 'confirmation' like this?

For example, if we have 1000 transactions in a mempool (sorted), 900 transactions are at least 10 minutes old, and we're confirming the first 720 transactions.

This may not be a perfect or complete solution, but we just need to find, 


Sort order; fee, size, etc.
Transaction age; say, 10 min
Confirm size; say, confirm first 80%


Note:
Sort order is based on f(trxn-meta-data; fee, input, output, etc.), transaction age is used as a filter. Another filter is first x% of the set.
Your answer assumes different nodes can have a consistent view of the mempool. If that were the case, we wouldn't need a blockchain at all, whose sole purpose is establishing consistency between different nodes' view of history.

The reason this is not possible is due to the laws of physics. A transaction tx1 broadcast in Australia, which conflicts with a simultaneously-created transaction tx2 broadcast in Alaska cannot be both included in a block. However, nodes in the rest of Asia will see tx1 first, and nodes in the rest of North America will see tx2 first. Which of those two is legitimate?

There is no solution to that problem, as due to general relativity, the concept of 'first' depends on one's frame of reference. A proof-of-work controlled blockchain solves this problem by accepting that not all nodes need to immediately agree on which of those transactions is accepted, and instead make economics force miners to make a choice between the to candidates.

Despite not having a guarantee for consistency between mempools, there is of course a very strong overlap. This overlap is exploited in many of the proposed efficient relay protocols, including the Relay Network, IBLT, Block network coding (and Compact Blocks which you reference).