Regular (non-bullet) trains?

It seems nearly all foreign travelers use the bullet trains exclusively, typically with a JRP. At least that's the impression I get from this and other websites. Is there some specific reason for this? Of course I understand that the bullet trains save a lot of time, but on the other hand it seems to me that once you've paid for the JRP, it's the JRP itself that makes you move on pretty quickly from one place to the next, since you'd want to get the most out of the pass.

What if I'd like to travel at a more leisure place, e.g. spend 2-3 days in each place I visit? I would imagine that in that case buying individual tickets for regular trains might work out better. Or is a JRP likely still a cost saver, even when using regular trains? Or is there some other reason that regular trains aren't a good idea for foreigners?