If a speaker requires an amp/ arc welder up front to drive it, then IMO, there is a problem with the speaker design. YMMV.
Exactly! Such speakers border on criminal as there simply aren't amps that sound like music that can drive them nor would they be all that musical due to thermal compression.
I look at it this way- if you can't drive it well with 100 Watts (in most rooms), its a problem. That is because the ear hears sound pressure on a logarithmic scale. So to get twice as loud (perceptually) that you can get with 100 Watt, you need 10x more- and 1000 Watt amps that sound like music don't seem to exist although class D is getting close with amps that can make 600 Watts or so.
The problem (again) is getting enough Gain Bandwidth Product in the design such that it can support the gain of the amp along with the feedback it has (together, known as 'loop gain'). If not, and this applies to almost all amplifiers ever made prior to about 2000 or so, you get distortion rising with frequency with its attendant unpleasantness- this is a good portion of the reason feedback has gotten a bad rap in high end audio.
Its not feedback's fault so much as poor execution of feedback.
Plus a 1000 Watt amp would not be able to make up for the thermal compression that would be present- as I mentioned before, as you try to turn it up to get around the problem, it just gets worse.