Amplifier current vrs watts; why is current more important?

As a Magnepan owner I will tell you I went through a couple amps trying to get the best out of them.  Maggie's are notorious for chewing up lesser quality amps and spitting them out.  They literally put one amp of high wattage into protection mode within 5 minutes and cooked the power supply.  I had a couple of monos built with about 220 watts but monster current and I finally heard all that the Maggie's had to offer.  Too much emphasis on watts.  

George - The " tone control" effect you speak of is due to output impedance of the amp. 
Man so much misinformation on here and the question was simple. The answers are going way off topic. 

I have the so called "easy to drive" Legacy Focus speakers because of their high 98 db efficiency.  But their low impedance (subsequent 20/20s were more difficult to drive) and 4 ohm preference make them difficult to drive.  Maybe it's their 3 12" woofers.  Anyway, an EAR 890 amp has great difficulty in driving them, lacking in bass and dynamics and just sounding pushed.  It's a Class A 70 watt design.  It sounds excellent on the Legacy Signature IIIs which have 3 10" woofers and slightly easier impedance curve.  

I can drive the Focus speakers with a highly modified 35 watt Dynaco 70 which has an electrolytic cap the size of the chassis underneath as opposed to the original.  Lots of power stored in that cap.  They're plenty the Sig. IIIs.  For the Focus speakers, I use a pair of 130 watt tube monoblocks, custom made, with 2 3" X 7" storage caps, huge compared to the tiny row of caps found in the EAR 890.   I  bet my big amps could drive most any speaker despite the limited wattage (although tube watts are 2 to 2.5 times more than SS watts generally, not including  Pass amps or other high current ones).

The " tone control" effect you speak of is due to output impedance of the amp.

Yes, this also as well on top of current starvation we’re talking about.

Any amp that has low damping factor, (output impedance is that high) should not be considered as well if one wants an amp that will not sound "coloured" and stays flat in frequency response.

Cheers George

Even though the OP’s title is
"Amplifier current vs watts; why is current more important?"

Just to take it off topic as oddio did, with his (excuse me) even grosser misinformation.
To show why output impedance (damping factor) is not the only cause for "tone control" behaviour, but also "available current" is just as if not more important.

Here is a typical case where "current" ability is the factor to making a flatter frequency response, more so than output impedance (damping factor)


Here are two very similar (save for their current ability) amps solid state linear each 60w into 8ohms, but their output impedance (damping factor) is more that 10 x different from each other, these are frequency response measurements (black trace) into exactly the same Kantor simulated speaker loads.
NB: Make sure you see what the graph graduation scale is for both.

1: This Budget Schiit is the one with lowish current , but the "best" lowest output impedance ( best highest Damping Factor) of DF=226 Output impedance=0.03ohm It’s FR is +- 2db
https://www.stereophile.com/images/416Schiitfig01.jpg

2: This Pass Labs one with high current but, worse 10 x higher output impedance and worse 10 x lower damping factor especially in the bass, and yet has far better control over the same simulated speaker load. It’s FR is only +- 0.025db!!!!
https://www.stereophile.com/images/1116Pint60fig01.jpg

As you can see the one, 1: with the "best" lowest output impedance (highest damping factor) is the one behaving like a "tone control" more that the other!!!!!!.
This is because the Schiit is current is limited into the low impedance loads of the simulated Kantor speaker load compared to the Pass labs.

Now back on topic, sorry hiendmmoe

Cheers George