The point of these sleep schedules is to get rid of everything other than REM. Numerous people, including several on this thread, find that after a couple of days of this, they go directly into dreams. That much works. The question is whether getting rid of everything else is sustainable and useful. Incidentally, I have known one person who naturally only had REM. He had problems and was diagnosed with narcolepsy. I have known several other people I suspected were similar, but who hadn't been through sleep studies. ETA: also, he found short naps quite useful.
After reading your reply, my impulse was to shrug and think "that objection is wrong, but I still don't think it's a very good idea." I since realized that what I had written really was my true rejection (besides a blind appeal to lack-of-popularity) and I didn't know otherwise about the success or failure of polyphasic sleep, so I'd better go look it up or risk missing out on some possibly-low-hanging-fruit.
Anyways, I'm still reading through PureDoxyk's blog, but I've seen that it definitely seems to work for some people. I plan to continue to look into it and decide whether I want to try Everyman once I go back to college.
I retract my previous comment. Thanks for the correction.
My friend and I are starting the Uberman sleep schedule (six 20-minute naps spread evenly throughout each day) tonight. Have other lesswrongians experimented with alternate sleep schedules? Are any of you qualified medical experts who can give input or advice? Success stories and failure stories would both be appreciated, and I'll keep you guys posted on our progress.