Also I think cutting ANY of the song's duration isn't great game design IMO
Sort of, but the main purpose of it is flexibility - if all three songs were 40s long, for instance, you'd be unable to leave a song slightly early without incurring songless time. Since they want the cycle to be 2 minutes, there's not really any option (barring use of some wacky number) besides to make each song 45s. And then the weakest one will always be cut short in practice.

I wonder if SE actually knows that people dislike AP. It appears as though they only just now realized how many people hated multi-dotting (even if plenty like me were fine with it), so it makes me think that there might be other things (a la ping) that seem like common knowledge to players that SE just isn't aware of.