It absolutely matters whether it's a new address every time or the same one. On-chain data is forever, most other data is not. Lightning zaps have plausible deniability. On-chain zaps don’t have that property. On top of that, Lightning has certain privacy guarantees after receival that on-chain does not and will never have. If you move the money on-chain after receival, everyone will be able to see it and prove it without a doubt. Once more, plausible deniability goes out the window. “Don’t transact with them.” Ok, here’s a thought experiment: If I want to make someone a target and I have money, I can just on-chain zap them 100 BTC. The fact that they don’t move the money won’t help them, they are still a target.