Conversely my club has a very strong junior section, and they all wear spikes for cross-country and track.
Trail shoes are lousy in traditional cross-country races, there is a reason why everyone wears spikes. Spikes are narrow, light, and cut through the mud, so the pin bites properly into the ground underneath. Trail shoes tend to float on thick mud, clog up, and turn into a big heavy mess. They’re designed for a very different thing.
Fell running is an oddity, with shoes like Walshs, but that’s because they work well in the peculiar conditions of fell running.
A pair of basic spikes will be under £20 for children, the pins can obviously be re-used in later shoes as they get older. Local clubs like mine run swaps where kids donate their old shoes to the club, and borrow another set. It’s also possible to use XC spikes on the track as well to get more use from them.