[brudgers]

From C the first six stacked fifths give C Lydian, not C major. (You get an F#, the 5th of B as the seventh pitch, not F the 5th of Bb).

You don’t get the perfect fourth until you go all the way around the circle of fifths.

You cannot stack perfect fifths and get a major scale.

[dhosek]

I was being sloppy and should have said diatonic scale.

[brudgers]

Sloppiness is why music theory is not scientific.

You can’t get to a scientific rationalization of the primacy of the major scale without it.

[acjohnson55]

The primacy of the major scale happened many centuries after the diatonic scale came to be predominant in Western music. The primary development that led to major tonality was the acceptance of thirds as stable consonances. As that happened, the Ionian mode (previously little used) began to stand out because it happens to have a tritone (B and F) surrounding its tonic major third (C and E). This is the core feature of the authentic cadence which gives us the tension <-> resolution progression that characterizes tonal music. Tonal music practice and theory develop in all sorts of interesting ways, spilling out from that basis.

The transitional period where this happened is roughly in the 1600s.