I don't agree, even an "awake nap" can be refreshing.

yes absolutely. Its only risky if you are a polypahisc sleeper and rely on these naps as part of your sleep

Also, just being a polyphasic sleeper is risky.

If you can't go almost right to sleep, then you weren't tired enough to need a nap in the first place. The only time I ever toss and turn is when I need to keep to a schedule and go to bed before I am fully tired out.