Is, IVs and Vs are the mainstay of Western music. Not only used for kids' songs, but an awful lot (and a lot of awful) pop songs. Most 12 bar blues use those three, and a lot of other songs can be played using only those three (I know, I've been to bars in Teneriffe!).
A lot of those songs can, and are, re-arrangeable to incorporate other harmonies - 'Happy Birthday' is one such, and probably benefit from that. Those three chords are the basis for music as we know it, and actually, a heck of a lot of other songs can be harmonised to only that. The 'happy' factor is maybe a contributing point. Who wants kids to hear sad, miserable, serious stuff? They've enough to make them cry already. I know; I was one - once...