I disagree with this statement. I manage a reasonably good-sized OLTP system. I wouldn't even want to think about trying to manage it without good indexing.

Inserts might be a bit faster without indexes (I'm not going to argue that one too much, but some of my testing shows that inserts into heaps aren't always faster than inserts into indexed tables) - but in a multi-user system with applications and users requesting information from the same tables that those inserts are running against, the performance hits to NOT index those tables would be awful.