I think one of the primary issues with popular music is that it's often ambiguous whether it's in a major or minor mode, even when the song starts on a minor chord. Classically, one would mark the transition to a minor mode by the existence of an authentic cadence: V/vi -> vi, or by the raised scale degree 5, but neither of those clues exist in either song that you mentioned.
In songs like My Heart Will Go On, it appears that the verse tonicizes I, where as the chorus centers around the relative minor. However does it make sense to say it switches modes every time the section changes? Maybe not
Good points. Many rules in popular music come directly from classical music (after all, it's been around for a while).
However, as you can see in the Hooktheory database, there are many progressions that seem to be unique to popular music.
You mentioned iii->IV, which is a no-no in classical music due to the parallel fifths (more common: V/vi -> IV). But also look at progressions like: C G Bb F, which is extremely common in pop. Here we have a double plagal cadence set up by the dominant that was never used by Bach or Mozart, which is probably best functionalized as: I V IV/IV IV
Hooktheory stores all of its chord progressions in relative notation so we have tools to answer questions like the one you've posted here. Although the Hooktheory database is relatively small, we have 20 songs that contain I vi IV V, compared with 100 songs containing I V vi IV. Just by visual inspection, of the songs that contain I V vi IV, none of them were written before 1975, which may not prove, but certainly supports your claim.
Right, all of the songs were normalized to C, which exactly the point. At Hooktheory.com you can examine all of the songs in relative notation (i.e. I IV V in place of C F G) which makes it easier to compare chord progressions without having to bother with their respective keys.
Exactly. D Major chord is a V/V in C Major, which has only a couple of common uses in popular music according to the Hooktheory database. V/V -> V7 -> I is one common one. Another is a substitution for ii, like: I -> V/V -> IV -> V, see John mayer, Kelly Clarkson, Kenny Chesney etc.
In songs like My Heart Will Go On, it appears that the verse tonicizes I, where as the chorus centers around the relative minor. However does it make sense to say it switches modes every time the section changes? Maybe not