If I just send fake letters, it's illegal (I assume). If I have a legitimate website selling logos, and point to the product page for the logo I accused you of copying, and I can claim copyright ownership over AI generated art, then I have the law on my side even if I get taken to court (I assume).

I'm not a lawyer though, so I'm probably wrong. At the very least, the legitimate website makes the threatening letter look more believable.