The benefit of dumbbells could be the opposite: that they weigh less than the body and thus make the exercises more manageable.
The only real downside to bodyweight training is lower back.
I learned this the hard way when I got back in the gym.
In practice it sucks.
Yeah ok, sure, you can make your push-up harder or easier if you incline one way or the other. But do you have a bench that can be set to the exact height you want? All padded surfaces? Do you have enough space? Not to mention your shoulder mobility/strength which might or might not be the best one for your push-up to work on all inclinations.
Do all people have enough dexterity and strength for all bodyweight exercises? I don't think so