Power lifting can quickly become anaerobic, when you run out of oxygen. But, weightlifting is used for more than just peak power. Many activity's benefit from pure strength, but most people are trying to improve both power and endurance.

Longer cool down periods (3-5 min) helps build strength faster and let's each set be more anaerobic and higher weight, but short cool down periods and slightly lower weight adds endurance and strength, plus more repetition.

The other benefit of aerobic weightlifting is you can better learn to minimize anaerobic activity. Full power all the time seems great, but being dead on your feet in 30 minutes is rarely useful.

If you're not in into the anaerobic zone, I don't think you're really weightlifting. You're dropping the weight so low that you're just doing cardio.

There is plenty of Oxygen to handle a single lift. Just not a rapid full set at near max weight. The specific transition point varies based on a wide range of factors,mbit simply waiting between each individual lift is enough to stay aerobic.

I'm skeptical about how aerobic weightlifting can be before it isn't really weightlifting, but also not too interested in arguing. Some weightifting protocols such as German volume training do seem like they must contain a decent aerobic proportion.