The problem with reflectors is that they are not low enough maintenance for children. They are cheaper for the same light collecting ability, but you absolutely cannot expect a kid to be able to collimate one and they are not nearly as rugged as you would like.
This means the parent becomes the gatekeeper of reflectors. The telescope only gets used when the parent is willing to set it up.
Refractors cost a bit more for the same aperture, but they are so much closer to point-and-look rugged and low maintenance. 90mm refractors can be had for $150 which are more or less equivalent to 100mm reflectors in regards to light collection. If the tripod gets knocked over by the child you will cringe but it is unlikely to be damaged unless this happened on concrete.
Someone above had mentioned low-magnification large-lens binoculars and I think that they are probably a much better introduction, as they are also rugged and low maintenance but have the added advantage that they serve useful purposes in daylight. Many are made especially for astronomy and come with tripods (a critique of one of the replies was the incorrect assertion that telescopes have tripods and binoculars dont.)
Low magnification isnt a downside. There is very little to really see at high magnifications unless you have a telescope with really good optics, which is not happening on a budget and isnt recommended for children. Sure, rings of saturn... a few moons of jupiter.. and then nothing else really benefits from high magnification on a budget. Meanwhile the sky is filled with nebula...