Either you don't, or you aren't paying attention to what you are saying...
PROBLEM 1: There are no addresses in the blockchain.
PROBLEM 2: Not every possible script has a matching address. What will you do with scripts that can't be converted to any of the standard address formats?
PROBLEM 3: A transaction that is confirmed AFTER this blob is added, but which refers to an earlier transaction that no longer exists? How will that transaction be verified?
Those are the first three issues that immediately come to mind.
But his transaction doesn't provide an address. It specifies an earlier transaction output. However, you've eliminated that output. Therefore, how will the miners know what the public key was at that earlier output which is now gone?
This does nothing to increase the transaction rate.
There are other solutions for that. If you want a trustless solution, use Lightning Network. If you are willing to have a trusted third party, then off-chain accounts will work.
Transaction history is already compressed pretty well. If you don't need the history, you can run a pruned node. You don't need to keep the history unless you want to help others start up new nodes.
No thanks. Take your TheftCoin scam system elsewhere. I don't want anybody deleting my money.
Go for it. Create an altcoin with your system. See how it works out. By the time you've worked out all the problems, you'll probably find that you end up with something that looks a lot like Bitcoin.