Well, we all know a sub has a larger voice coil. More copper is going to be less I squared R losses than what you'll find in a smaller driver. You might find a 1000W rating on a sub with a 3" voice coil, but you'll not find it on a tweeter with a 3/8" voice coil if that. Plus a sub has forced air cooling, and will radiate thermal energy to the basket, poles, etc.
Now this should be a relatively common amp:
NEW US AMPS 4000 WATT MONO CAR STEREO SUB AMPLIFIER AMP - eBay (item 350096784756 end time Sep-18-08 18:36:32 PDT)
1500W, 4000 peak? If you notice, there are 75A worth of fusing on that amp. If it really did big power for long durations, the most that amp could make at fuse rating is 15V (maybe) x 75A = 1125W. Maybe the fuses are a subject to tolerances, and maybe you might squeeze 1200W out of it, but not for long. But the commonly accepted fact is that this energy doesn't last in durations long enough to blow those fuses, unless you are listening to Bass Mechanix or something like that. And most music does not contain notes like that.
Yes, the subwoofer requires and uses more power than any other driver in a system (typically). But you must feed it clean power, like any other driver. The fact that humans can't discern distortion below 10% doesn't mean it isn't there and isn't troublesome. And it's much tougher to detect at bass frequencies, in fact I'd say damn near impossible even for trained ears. This is also what makes this an issue. You can hear it quite easily at midrange or treble frequencies, and adjust your system accordingly.
It's pretty easy these days to know the mechanical limits of your speakers, as big power (cough!) is relatively cheap (clean is another matter entirely). Once you can reach those, it's easy to control. But when you underpower a speaker, you may never reach the mechanical limits, but instead bombard it with useless and wasted energy that must go somewhere, and is manifested as heat. Heat kills, speakers are only 1 item in a long list. Clean power also must go somewhere, and can also be manifested as heat, but we equate loudness with distortion (6x9's off deck power anyone?), and when we detect loudness (distortion in many cases), we tend to want more, becoming immune. Or the sane folks adjust levels to avoid those scenarios.
When I did car audio as a living (the 1990's), big amps didn't really exist, or were affordable. Folks wanted 150dB on 1000 watts, but the amp was $3K. So, lower power and multiple drivers was the norm. And we had lots of warranty claims back then, on all sorts of drivers, but mostly subs.
I'm sure subs have become "better" and amps "bigger", but too little power and an itchy "volume-up" finger is as much a problem today as it ever was back then.