You do caching so you don't always have to go back to the DB is the main thing. The other interesting capability is light scripting at the edge. Think "this page is cached but I'm going to add in a custom username".
There's some more exotic stuff around sharded database locality. But I'll skip over that because distributed mutable state is hard and its not my specialty.
Connection warming and shorter tls negotiation round trip times are also a thing but probably less important compared to the database thing you are mentioning.
But mostly this architecture makes sense if you can do some caching or if you're doing more data/log collection stuff.
For prior work see ESI (edge side includes). Assembling stuff at the edge does have some benefits but it has been hard to create a good interface for that.