Actually, the O2 is on a timer, at least for OBD1 setups. It is a fairly long time. With the heated O2, if the engine can stand the leaner 14.7:1 (ideal) mix of closed loop, you can modify the timer for the O2 so that the ECM goes closed loop much faster. IIRC, engine temp needs to be around 120-140* before one of the criteria for closed loop is met, along with the timer.
Short of all that, the reason MOST go with the heated O2 on an otherwise completely stock setup, is that when swapping to headers, the O2 sensor either doesn't heat up enough to go closed loop, or only heats up when the engine is under load. That means at idle, after cruising for a bit, your engine will "drop out" of closed loop. This would really hurt you, for instance, at an emissions test.