I remember when I used to take longer breaks of 2-3 minutes or so (and sometimes even longer) between sets. Taking shorter breaks definitely changes the tenor of the workout; it feels more like having gone through the wringer. Initially, I thought I might have to stop a set because of an aerobic bottleneck rather than hitting anaerobic failure. But that was not the case. Admittedly, I would likely do another rep or two if I waited long enough, but I'm not sure what the upside of that would be. I'm still going to full concentric failure rather than being aerobically gassed out.
Regarding your warmup sets, you're just using that as an excuse to rest.

Kidding aside, though, do you really need a warmup set for each different exercise you do? The reason I ask is because I thought so as well for the longest time. Unless you're going heavy on skilled movements, I would think a warmup set for the first exercise of each muscle group is enough, especially if you're using machines. And for us older guys, it's better to go with moderate weights slowly, in which case the first few slow reps of each exercise serve as a warmup. Just my opinion on what I've been reading and based on my own personal experience.
In fact, in my case, my ~HIIT cardio is my only (general) warmup, after which I go straight into my work sets.
But I respect your lazy ass if you feel the need to intersperse "warmup holidays" throughout your workout.
P.S. Obviously don't change anything if what you're doing feels right.