In banking, a settlement system usually is a system to periodically update a coarse-grained ledger with the an aggregate of finer-grained transactions.
Have you been introduced to the concept of "blocks"? (sorry, I really don't intend this to be mocking sounding, but I'm not finding a better way to put it). What you described is _exactly_ how Bitcoin works.
By "aggregate", I mean the net difference. Banks call this process "netting". For example if 1302 transactions moved 10 million from bank A to B and 917 transactions moved 12 million from bank B to A on a given they, they'll simply transact the net amount of 2 million over night in one single transaction. See
https://en.wikipedia.org/wiki/Clearing_House_Interbank_Payments_System for an example of such a system. In fact, this resembles the Lightning network, which also only transfers net amounts on the blockchain (if I understood it correctly). However, it is not how the Bitcoin blockchain works, because the blocks in Bitcoin still contain every individual transaction. There is no netting.