Too Much Power

I have never had a problem with to much power, only not enough. High power amplifiers will only damage your speakers if you exceed the rated power, and you can usually hear the speakers straining long before damage occurs. On the other hand, damage to tweeters and midranges occur much easier by clipping a low power amplifier while trying to achieve a desired sound level. I have started downsizing but once had 9600 watts rms. Only damaged tweeters when I clipped a 60 W/channel amplifier when I first started in audio.

are the drawbacks to that much power?

Size, weight, heat, and if the gain values are high perhaps a little noise but quality amps are very quiet today. 

Thanks. But as the 1200's are class D amps, size, weight, and heat would not be a concern.

I was answering what sounded like a more general question. 

Overkill in some cases perhaps but with modern amp technology no real downside, all else held constant, at least these days. It’s like an oversized engine in a car. Worst case you are paying for an insurance policy. In years past, extreme size, heat and weight were common downsides.