"As a graduate student, you would be better served spending your time squeaking out one extra "Tier 2" publication rather than being the professor of record for a course."
This is likely true at lots (but not necessarily all) R1s. That said, it is a poor strategy unless you are sure that you want to be at an R1, and that if you fail, you want to try again later (stay in postdoc) or leave academia.
If there is a chance you might be happy at a place that emphasizes teaching more and as a result you're applying to some of those places, it is a HUGE bump to your applications to be instructor of record ONCE. Quantity of teaching experience doesn't matter much even at very teaching-focused places, as long as you get just a bit in, including instructor of record. There are lots of schools out there that won't consider an applicant who has never been instructor of record, even if s/he has great teaching evals from being a TA and has great research mentorship experience. These might be places you don't want to work anyway, but if there is a chance you do, it's good to get that experience once. By the way, an R2 would not throw out your application without "instructor of record" experience, but many of them would rather you went from 0 to 1 teaching experience than add that one additional Tier 2 pub. Unless your publication record is thin so this one pub adds significantly…in which case you won't be hired anyway.