Hmmm. The tonic, dominant, sub-dominant and sub-mediant (or relative) minor. All founded on a fundamental harmonic relationship discovered by whom? – Pythagoras.
In point of fact, to those four chords there are only two others that belong in the major key – the supertonic and mediant minors. The triad built on the leading note and using only notes from the scale is necessarily discordant.
And, as a good example, to suggest that Let It Be is based on four chords is not accurate – they play only the briefest snatch from it – but certainly it is a good example of a great song that has an astonishingly simple chord sequence. The accurate sequence of the verse is
tonic
dominant sus4 to dominant
sub-mediant minor through dominant to
sub-dominant seventh
subdominant sixth
tonic
dominant…
and the famous four chords in four beats sequence
…sub-dominant,
tonic first inversion
super-tonic seventh
tonic
There are those who might argue that the penultimate chord is actually the second inversion of the dominant thirteenth, but that is based on theory that Paul McCartney was almost certainly unaware of.
One fabulous example of a truly great song that is based entirely and exclusively on those four chords but demonstrates just how powerful and original they can be is Marc Cohn’s Walking in Memphis.
I’m not doubting the formulaic nature of the vast majority of ‘hit’ songs, but I absolutely am doubting that you can judge the originality or formulaic nature of a song purely on the simplicity or complexity of its chord sequence. There is a song by Sam Baker called Waves. A large part of what makes it such a good song is the painfully moving lyric. But from the list of chords you can remove the sub-mediant minor – it uses only the tonic, sub-dominant and dominant chords. (It’s in D major so the chords are D, G and A.) Yet from that he fashions music that fits his lyric perfectly. It may not be everyone’s cup of tea, but one thing it most definitely is not is formulaic. I commend it to you.