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I'm talking about Christmas songs, Nursery Rhymes, and so forth. It seems to mainly be I-IV-V in a major key. Not necessarily that progression, I mean just those chords.
Why such a strong bias towards I-IV-V? Is it because when people communicate with children they tend to only talk positively, so only major (aka happy chords) are involved?
The fact that they are in a major key is completely to do with the fact that children's songs tend to be lighthearted and carefree (hence a major key).
The specific intervals you are talking about are very easy on the ear because of their predictability.
The perfect cadence from the V returning to the I is very predictable and easy for children to understand - it's satisfying to the ear. The IV chord has a note in common: the dominant of the IV or the tonic of the I chord. Eg. In the key of C major, the IV chord (F) has the note C as its V. This means melodies are very easy to shape. And as you know, melodies from children's songs do tend to be catchy.
Similarly, this chord progression is used in many pop songs due to this predictability (and so steadiness) and its ability to easily shape and support melodies.
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...
TL;DR
Why such a strong bias towards I-IV-V?
No bias per se; it just happens to be the most common owing to historical reasons.
Actually, chord I-IV-V happens to be a chord progression which is largely perceived to be an easy one to grasp; it is no surprise that it is the very common the world over and mainly used for various occasions, purposes, folkloric tales, children play songs just as lullabies (even babies can gracefully capture the feel and intended message) among others.
In Ghana for instance just as many other African country, the chord I-IV-V progression happens to be the "secret" ingredient of success for many gospel singers and even secular ones; hardly will you hear a widely common song, particularly African Popular Music, without this pattern.
