I’m one of those “no exercises” players. If I can’t eventually use it in my playing, I find I’m really unmotivated to do it. Of course, plenty of cool licks that do sound good can also work “as an exercise” if the technique is something you’re trying to learn. So it really depends what you mean by “exercise”.
In general, I think musical practice is the most fun practice. So yes, jamming with phrases you want to learn and use, that kind of thing. Your current best picking motion is a DSX / UWPS motion, so that’s the kind of phrases you’re looking for. Obviously the Primer has a bunch of those but they are a little more “pattern” oriented. You can still make them musical if you throw in a backing track as you point out.
However we’ll be adding more specifically genre-oriented phrases to the Primer over time, in the styles our viewers / customers are playing. Since you’re a country player, here are a couple one-off phrases we put up in the Channels section of the site that are entirely DSX / UWPS:
These kinds of lines can totally work for country. They’re just dominant lines. But the key here is that they are downstroke escape, so the fast motion you posted the other day will totally work on this with no string changing difficulties once you dial in the hand synchronization.