I think one of the challenges with exercises is that everyone has a different level of comfort, even toleration of them. For me, I come from years of playing a melody instrument (violin, moving to viola), so my skill at playing single notes far exceeds my ability to play pieces proper. I've also been in the local college orchestra for years, so that helps keep me honest about proper tempo.
When I started practicing more properly, I had to work to put the beginning of PH #2 together, despite being not far from sight reading most any treble clef melody with some speed. For me, I find the exercises are a good way to get concentrated work on areas I'm just generally weak, like RH chords and reading multiple notes ( without having to hunt down pieces that stretch those areas but aren't out of reach. Doing this, I can feel the benefits when I come to pieces that are more complicated, so that helps with motivation.
Like I said, I don't practice exercises according to rule. The closest I get to that is some scales that also serve for initial finger warm up. Beyond that, I have days I don't do any exercises, and others where I end up spending nearly a whole hour+ practice session on exercises.
If I hit a trouble spot in a piece, I'll often do like Tom does, and make up an exercise and spend several minutes on that right then.