HTryan
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
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.