So block 123,456 shows I (or more correctly an address I have) have a balance of 100 BTC.  How do you verify it?  If all you have is the balance how do you know it is correct?  If you can solve that problem then you can build a more efficient

Hint: miners might actually be attackers, scammers, thieves, etc.  In Bitcoin miners can't falsify coin records.  If they make a block which shows a "fake transaction" other nodes (which inherently DONT TRUST any other node) can verify the block is invalid a reject it.  How can they do that?  Because they can trace the history of every coin and thus can prove a tx is valid.

Don't start by thinking of how "X" would work.  Start by thinking of how someone could abuse/attack/defraud "X".  Remember this is money we are talking about here.