Why do speakers recommend amp wattage?

You could put a kilowatt in front of your Ushers without fear as long as you were actually listening as you turned it up. Running at 'redline' for extended periods will probably result in some kind of meltdown, or ear damage!
Low power at too high a level is probably worse, as noted above.

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Tradition, I suspect. Often, the impedence curve is more important.

Nice thread. I was also curious about the wattage.

What is the importance of "current" in amperes? I have seen specs of amps with wattage but different current output. For eg. one amp had 200 Watts per channel and gave 60 amperes where as another gave 200 Watts but 45 amperes.

Thanks,

The most practical reason is as a guideline to avoid distortion and speaker damage due to clipping by running an amp with too little power too loudly.

In general, solid state amplifiers that deliver more current (amps) are able to better drive most dynamic speaker designs with varying impedance curves at various frequencies (referred to as a "difficult" load)and deliver more balanced sound from low to high frequencies.

Duh. The more Watts listed on a speaker, the louder it is. That's why I only buy White Van speakers. They are always, like, 250 Watts and really rock the house. Way better than that Bose crap.