Back in antiquity, I had to "register" to get a "bikes on trains" permit to carry my bike on the metro. It was a nominal $5 fee (covered the cost of the photograph) and a royal pain to go to the downtown office to get the permit, but the whole point was to educate the permitee about the dos and don'ts of carrying your bike on the metro. Then, whenever somebody it being a bonehead with their bike on the metro, the officials can say either: a) "You need to have a permit to do that, go get it." saving themselves all effort at education on-the-spot, or b) "I see you have a permit, but you obviously didn't pay attention to the training." and possibly revoke the permit on-the-spot, forcing the ex-permitee to jump more hoops to get it reinstated.
Hunting and fishing licenses are a similar game, though their fees are higher, and annual. The presumption is that you will learn what you're supposed to know as a licensee - though, in practice, they're mostly just an annual fee.
Registering drones, like registering handguns, will give some traceability to the bits of electronic junk that get lost in hard to get to locations inside state/national parks, and on other people's private land. It might make some operators a little more careful and a little more aware of the impacts their toy can have. I don't think it's much about keeping them out of the flightpath of commercial airliners, I think it is about making the owners more accountable for less serious bone-headdedness.