"Why have a website generate your public private key to take to your client?"

The problem is people with no previous experience with public key cryptography will not be familiar with backing up secret keys. The goal with a website like start.njump is to make this easier.

I would also like to see more apps implement NIP07 that is more like a BIP39 experience. Current is the only app I know that does this though. Indon't recomend it anymore because the lightning addresses stopped working.