EVM is a deterministic meaning that if any two(or more) nodes receive identical transactions in the same order(which is what blockchain is for), they will arrive at the same state independently. And there wouldn't be any need for each node to execute all the code. Which would simplify everything to an order of magnitude and would allow each node to decide what transactions they actually want to execute.
As I understand the fact that we have hashes for each state allows us to make requests for the state with that hash to other nodes rather than computing it ourselves. So another question is how much computing does it saves? Is that approach faster? And would it be actually viable to try the approach I offered?