Why any transaction dont include the final balance of each address?
That would be much better to get the balance of any address, just need to find last move in blockchain and dont need to recalculate entire blockchain.
The reason behind the need to every full node have a copy of the whole Blockchain , including every spent input and output is that it's a system where you don't need to trust anyone. The lack of trust is one of the things that make this cryptography system so secure.