Question about high current amps versus "not high current amps"

Recently I read a reply to a post about a certain speaker, and the person who replied typed that (and I am going to paraphrase somewhat) the speaker required a high current amp to perform well and it wasn’t the WPC that was important.

Sorry as I am afraid that these are probably going to be  "audio electrical questions for dummies," but here goes:

I vaguely remember being taught the PIE formula, so I looked it up online for a quick review and if I am understanding it correctly,

P (power/watts) = I (current/amps) x E (electromotive force/voltage) .

My first question would be: if I am understanding that correctly, how can wpc NOT matter since watts are the sum of current x voltage? I mean if you have so many WPC, don’t you then HAVE to have so much current?

My next question would be, if I am understanding PIE correctly, is E/voltage going to be a fixed 110 vac out of the wall, or is that number (E) determined by the transformer (so it would vary by manufacturer) and it is that (different transformers that are used in different amps) going to be the difference between a high and a lower current amp?

Or am I completely off base thinking that P is wpc and P is actually the spec in my owners manual that lists "power consumption as 420 watts operate 10 watts stand by"?

And lastly, what would be an example of a high current amp and what would be an example of a low current amp?

Thanks.