Actually, you do if you'll exceed a certain height or if your rocket engine is larger than H (or perhaps I) class.
https://en.wikipedia.org/wiki/Model_rocket_motor_classificat...
Additionally, there are many stories regarding how current drone operators either ignore common sense regarding where to fly, or make mistakes that put planes in danger, or whatever. You can simply google "airline drone near miss" to see examples. Just because people theoretically could act in an intelligent manner doesn't mean we can rely on them to actually do so.
Ok, that's a bit pedantic - search for "airliner drone near miss".
But what are we talking about re: "near miss" here? The phrase itself defines as no actual impact. How many actual problems are we talking about here, vs "close but no harm done"? I'm just trying to bracket the issue.
I expect the absolute distances considered critical for drone operations to be smaller, but still significant.
The level of scrutiny involved in aviation safety is very impressive. I’m not actually involved in the field myself, but find the human factors and systems engineering involved in keeping the skies safe to be very interesting. NTSB and CAA incident reports make fascinating reading!
Many of the hits describe the specific near misses, thus answering your question.
But the question about how many actual problems we are talking about is missing the point. Drones are at an inflection point. People have been flying them for decades as a hobby (they were called "radio control airplanes" back then) without issue, but they're set to become far more popular, far more available, and far easier to use really rapidly. The question is not so much how many problems there are today, but what it'll look like in five or ten years, and how we can get ahead of any potential problems now.
close but no harm done
Are you serious? This is an airplane we're talking about. I don't care how close you think you are or aren't when you're flying your toy around the airport. I don't want the pilot of my airplane to be distracted by your asshat-ery no matter how much distance you think you have from the airplane.
Care to guess whether that was a zero or non-zero distraction as I passed the affected area?
Drones, not so much.
Or, rather, it's a great rationale if you have an agenda that needs more political support than it would otherwise be able to garner. It's not hard to imagine why governments would be utterly terrified of a civilian population with widespread drone ownership and ongoing development.
http://newyork.cbslocal.com/2015/08/03/drone-sighting-jfk-ai... http://www.cnn.com/2015/05/14/politics/white-house-drone-arr...
etc.. these are not hard to find. Now actual compendiums are being done, but I couldn't find the raw data. The FAA says it has gathered "more than 650" reports: https://www.faa.gov/news/updates/?newsId=83445
As a pilot, I do not see this as being surprising. People are doing dumb things with drones, just like pilots did dumb things with airplanes in the '20s and '30s, leading to the precursor of the FAA and the creation of the airspace system.
But the real reason for registration is so that when there is an accident involving a drone and someone on the ground, such as a person shooting down a drone, the owner of the drone can be identified.
Finally, if a drone gets involved in my airplane's propeller, it will probably be diced into chunks so small you'll never find all the pieces. However the propeller and engine will need to be rebuilt, at a cost of $20,000+, so you can bet that I'll be on the ground looking for those bits so I can stick that insurance claim.
It's not like drones are risk free - quad copters are like hockey pucks floating in the air and can easily drift or fall.
But that said, considering how many of them are in private hands and what most owners actually do with them, the registration requirements are completely onerous.
You don't register to shoot off a model rocket at the park, you don't register to hit a baseball at the park, and it's accordingly totally not clear why you need to register to fly a small aircraft at the park when it's pretty much going to stay lower than maybe two and half telephone poles.