Most kite festivals consult the CAA for permission to fly above the allowed 200ft ceiling for the time of the festival, I've been witness to a few aviators who have totally ignored this and crossed festivals at dangerously low levels. I've also seen a few just testing the area, flying at the ceiling to make sure the kite flyers were keeping their side of the bargain.
Single line display teams tend to fly kites bigger than most aircraft, usually with a lifter kite 100ft above to aid stability. One large kite flown at 1500 ft AGL is often used as a beacon to advertise the event.
Most festivals have various competitions, Rokakku fighting tends to take place at 200ft or lower, but the kites can be up to 5m, because they are rigid kites, losing one can be a bit problematic as they will drift a long way, especially if there is a lot of line to give drag.
Indian fighting kites are made of tissue paper and bamboo with a span of under 1m. They tend to be flown up to 1000 ft on cotton line. In organized competitions, the line is coated in a glass paste designed to cut the opponents line.
Altitude sprints usually have a set time, say 30 seconds, where the kite is launched from the ground and the winner is the highest kite at the end of the time limit. 2000 ft is attainable in 60 seconds. These competitions are open to any kite, but specialist altitude sprinters are usually under 2m.
Most display kites and competitions are well within the ANO, unfortunately, a small number of people, both at festivals and privately, set up a kite on some weird and wonderful anchor system designed in the shed, then leave it unattended at a ridiculous altitude. At festivals, shouting a few expletives and carry a knife to cut the line, normally sorts these out. Private individuals are a bit more problematic. One particular person in the midlands, at least five years ago, stated his intentions to fly as high as possible wherever he wanted, he was banned from any festivals and clubs,.
Sport kites, dual line ballet and quad line don't fly on anything more than 45m lines, power kites for buggying and surfing don't go any higher than 60m.