Plane Sailing
Astral Admin - Mwahahaha!
Just out of curiosity, why do you want to do this? A long time ago I played AD&D with rollling initiative every round and it was horrible. The time spent rolling dice, the illogical things that happened because people took two turns in a row...
The funny thing is, this was the standard way of doing combat in D&D for, what, about 25 years?
When people heard about the cyclic initiative of 3e people threw their hands up and said "Wuh?!?"
The fact is, rolling for initiative works. Cyclic initiative also works. Deterministic initiative (e.g. Bushido, Runequest) also works.
There are different wrinkles to each approach, and as long as everyone playing is happy with those, you can go with whatever seems fun.
Doing it in 4e would be interesting. As has been noted it means that sometimes some powers would fizzle early and sometimes those same powers might seem to last twice as long (unless you made a change like 'power lasts until end of next round', for instance - and possibly applied damage to everyone at the top of the round and did saves for everyone at the end of the round). Whatever King Nate chooses to do, it will find a natural balance point in the end.
Cheers