It all depends. Mostly I don't toast the bagel, but when I want a little crunch added to the chewiness of the crust and the softness of the bread, then I'll toast it. What is difficult is finding a bakery that really knows how to make a bagel. It's a bit more complicated than some breads and it's really a balancing act.
The bread is more substantial than Wonder Bread, but not so much that you could lob a bagel at a battleship and sink it. That's why knishes were invented. The crust on a well made bagel should have a satisfying amount of chewiness.
Unfortunately, like so many good things, the bagel has been mercilessly commoditized, made to jump through hoops that no enlightened society would ever countenance. Chocolate? Strawberry? Gad, they might as well be biscuits! Not that I don't like biscuits, especially a beautifully tender one, but a biscuit is only a staging area for gravy and other goodies, it's everything else's bitch. On the other hand, a properly made bagel can be quite self sufficient. It has self respect. But all these flavors! Sun dried tomato? It's Western Civilization's nether bits!
Real bagels come in a handful of unfooffy varieties, white, egg, onion, pumpernickel, sesame, maybe poppyseed. After that, the slide begins gently with cinnamon raisin, and then the steep fall into the hell and damnation of chocolate bagels, sun dried tomato and the truly horrid pumpkin spice. I blame Manhattan and Noah's, two of the worst bagel makers in the history of bagel making. Noah's bialies weren't bad, but it's been years since I've been in one of their stores, so I can't attest to their current quality. You couldn't tell the difference between the bread and the crust. It was all a dense bore. And truth to tell, there isn't a chain that's going to do it correctly. Bagels need a bakery that makes them with love and respect. Good luck finding one.