I tried using a small lodge cast iron griddle plate on my genesis but it was a pain. The Lodge just couldn't stay hot with the lid up. Especially with the Genesis 1000 I think there's just too much steel in the flavorizer bars in the way. No one wants to use a griddle with the lid down. I love a grilled burger but there's just something about a smashburger that's hard to beat. Plus, it's easy to get some caramelized onions going, get your buns toasted, etc. Being able to make cheesesteaks is amazing. Making breakfast for a lot of people is great. You don't think you'll need to space of 36 inch wide griddle, but you'll use it if you have it.
I think the build quality has to be better on the Weber. The Blackstone is pretty chintzy, but I keep it covered and I keep the griddle seasoned. The burners are exposed to zero grease. It'll probably last me a LONG time where I'm at. The advantage with Weber is parts availability, etc.