Even if they do, they're mostly cardboard, whereas model airplanes have things like small engine blocks. I bet a 737 engine could ingest a model rocket without anyone noticing.
Even though the FAA has engine manufacturers like GE test the hell out of engines, it's tough to predict what will happen in the real world. Birds are a huge threat to aviation, both engine ingestion and windscreen collisions, and birds are mostly organic. (It goes without saying to stand the hell away from an operating jet engine even at idle, too, because humans do get ingested with fatal results.) I can't imagine an operating engine ingesting a drone or anything else with non-organic components would go well, and this is why I always advocate very strongly for safe drone operation.
Here's an intentional intake blade failure to ascertain whether the engine can contain the failure without threatening the aircraft; this is useful to see what happens if something is ingested that causes a catastrophic blade failure: https://www.youtube.com/watch?v=WAhjSviYVr8
Routine 400+ foot launches are more the purview of dedicated rocket launch events, which typically do go through extensive FAA clearance and such, and which have certification processes in place for those flying all but the lowest-powered rockets. Airspace is usually sanitized, and for good reason: these sorts of rockets tend to be much bigger than your ordinary backyard-launched Estes rockets, and very well could do significant damage to an airplane should a collision occur.
Tip: if you want to fly in a baseball field, and get your model back (not drift out of the park), stick with engines like "B6-4" or "C6-3" and models sized for those engines. If you fly a C6-5 or a D12-7, you had better have a good size farm to land in and a few friends to help spot :-)
http://www.hobbylinc.com/rockets/group/enginefacts.htm
Flying G size engines and up? Go to a special event in Nevada. Those can go a few thousand feet up. (or lift some heavy/dangerous frameworks)