“You can’t get REM in any normal “nap,””
Speak for yourself. If I nap for at least 1 hr 20 minutes, I can get a REM cycle in.
“you don’t need it to be rested during the day”
No, not normally, but if I do take a nap, I’m going to take one that doesn’t leave me feeling more tired than before I took it.
A 100 minute nap merely gets you ten minutes of REM sleep:
https://www.webmd.com/sleep-disorders/sleep-101
100 minutes is not a normal “nap.” That’s better described as “sleep.”