Yes, your low frequency driver, or sub is what needs the power. I have had a chance to see center channels in large mode, power amp with meters, peak hold types, and have yet to see them hitting in mid double digits without needing earplugs
Subs on the other hand have been hitting in the low hundreds at the same time.
So, I would not worry about it. Remember that tweeters, most of them are rated in the low 2 digits, 20 watts or so before they start to fry.