There's a difference between average listening levels and peak transients. While one or two watts may be all you need most of the time, the transients like drumbeats need much more power, sometimes as much as hundreds of watts, to accelerate the speaker cone or diaphragm fast enough to sound exactly like the real musical instrument, or at least as close as technology permits.
Voice coil overheating is not a factor in these instances, because they last for only fractions of a second. However, if your amp or amps cannot put out the needed power when it's called for, it's not possible to have truly realistic dynamics.
In my opinion, it's best to have an amplifier that has both high peak power available when needed, and very little noise or distortion in the under-10 watt region where it will usually be operating. It's difficult to find an inexpensive amp with both of those characteristics.