Why do speakers improve with more powerful amps?

Power supply

Power supply

Power supply

Bigger amps have bigger power supplies. The signal that gets sent to the speakers, is fed directly from the power supply. Bigger power supply, more dynamic headroom. 
 

My 30w class A amp, with a massive power supply - 192uF of capacitance and a 500va transformer, more than adequately drives my 80db 4ohm speakers. 
 

An amp needs a power supply that can handle the difficult passages in a piece of music. 
 

I agree w the comment above where an amp should work within its linear region. And to make a big power amp that is operating in an ideal manner at low power, takes some skill. Having two output transistors per channel vs 16 per channel has some benefits.
 

So many variables when it comes to having great synergy between amp/speakers.
 

There is a dynamic load being presented to a reactive source with an ever changing signal. 
 

Bigger isn’t necessarily better. Better, is better.  

@perkri 

Amazing answer very helpful. Impressive how you drive inefficient speakers with so little. Worthy of study.

That's a really pretty Marantz vintage piece.

@emergingsoul 

Yeah, quite surprised myself! I have also driven them with great success using a single ended solid state VFet amp (Pass DIY) which is rated between 8 and 10 watts. 
 

For fun, I got one of the Fosi V3 amps. It, is rated at 300w into 4ohm. (Complete BS…) Hooked it up to the speakers, and it was turned up to 3 o’clock on the dial, at which point it was distorting and no where near as loud as the 30W at 10 on the dial. 
 

it’s a learning thing…

And thanks, the 7T is a wonderful, and surprisingly good sounding pre. Unfortunately, the right channel died, so now I have to pull it open and figure out which bit when bad…

I value quality over quantity in wattage for amps.  Blessed those who need 500 or 1000wpc, but for indoor listening, 10wpc is more than I'll ever need.