Point one, it’s good to have multiple tools in your toolbox, so unless playing the exercises “Paul’s way” is super frustrating, I’d try working them his way and see how the progress goes.
I’ve seen Paul crow about his curriculum there being the most organized he’s ever done, and informed by mistakes he’s made from earlier experiences teaching. Now, some of that could just be marketing spin, but Paul seems like the kind of guy who would plant seeds in early exercises that are meant to bear fruit later.
I would skim the entire course, and try to understand where I think he’s going. Figure out whether he’s leading you into advanced licks that will demand one picking strategy or another, and figure out whether there’s genuinely a need to “repurpose” his exercises through your own CTC lens, or if it’s worth working through them “at face value”.
Life is short and there’s no point rigidly following something if there’s strong evidence it’s not working for you. But at the same time, be sure you’re honest with yourself about whether you’ve truly given it a fair chance to work before you give up on it.