We should reject hard-to-drive speakers more often

This thread got seriously above my IQ this page, I've been able to play in waters previously too deep because my family took care of me in their passing and I was living within my means before that. Anyhow I learned the hard way about how dull and lifeless a pair of speakers can sound without enough juice. 

Here's where I get confused and I hope somebody can explain it in simple terms. Why does huge power matter when I'm listening between .5-5 watts? My speakers sounded dull and lifeless until I turned the volume past 90 db so I swap out my 300wpc and replace with a couple mc 611's and suddenly low volumes sound dynamic? Shouldn't any amp have power to spare at 1 watt?  I've shipped several very highly regarded speakers out because 250 wpc wasn't enough to 'wake them up'. I only mentioned the mac model because IDK if output transformers on a SS amp are a factor in my question.

@steve59 

https://youtu.be/AhB8uL12gtk

this may help...

... also don't confuse input sensitivity of an amplifier with its power output

I watched the video, not sure PM did the job of explaining the difference between the quality of a Cambridge audio watt vs the BHK.  How would somebody confuse power output with input sensitivity or is input sensitivity a possible reason for the low volume differences I'm hearing?

My speakers are Kef Blade 1. When my 250/425 wpc amp drove them to realistic levels I thought I was golden, but as time passed and I found low volume listening was boring I decided to borrow a more beastly product and the Mc 611's are staying. I think of the Horsepower vs torque analogy but have no clue what amp measurements would apply?