That collaboration and cooperation often counts as cheating in our education system is a stupid relic from some hundred years ago.

If you want to mould a Taylorist's dream of obedient, quiet factory workers who spend their lives making the left side of the head of a pin then yeah, go ahead and discourage cooperation.

For anything else? Especially the creative work that will be expected of current students in the future? Cooperation should be a major goal of education.