Why not nodes just keep track of of bitcoins and where they are? Like so:

Alice wants to send Bob 1 btc she does so and alerts a fair amount of nodes that she did this. The nodes then collectively agree that bitcoin#1251262613616 is now under the control of whatever address alice sent to. Sort of like a database with two columns, a unique ID column, and a proof of ownership column. Mining can still be a chain, but it would be much simpler considering that each block now doesn't have to store transactions. With this system, mining now is piece of cake, no need to process transactions, no need for large block chain. Transactions are as instant as the propagation on them.

Pardon me if I have something wrong technically, I'm beginning to understand how bitcoin functions cryptographically.