Why do speakers improve with more powerful amps?

Through the years I've went from 80 watts, to 140, to 200, to 300 and now at 600 and 1000 Amps. (Legacy IV 2 and IV 5 Amps). At normal listening, like a movie at slightly spirited volumes there is a difference, although slight. TURN it up, like listening to a Video Concert, and there is no comparison. One sounds like a recording, and one sounds like your THERE! 

While it is fun to talk about our hobby, there are tons of opinions out there but it is up to each individual to decide what works for them.

No one would deny that "each individual to decide what works for them."

The point of these discussions is to understand some of the scientific principles so that individuals spend less time looking for needles in haystacks. Thus, it’s not just frivolity ("fun"), it’s about community inquiry and fact finding, where possible.

The conflation of inquiries into facts with some kind of abnegation of "individual decision making" is sort of dystopian; why would anyone suspect that?

@hilde45  I agree.  I've had a couple folks tell me in the 10's Dahlquist group TELL me I need 200 wpc and my amp will never drive them to their capability.  MY ears know what I'm hearing. How would they know? LoL  And being musicians ears that have listened to music since I was 13, I trust them.  I'm 68......

@carlsbad2 +1

I have a 450wpc amp that is outperformed by lower wattage amps. Many things are more important than power. This realization has me on the waiting list for a SET amp from Decware and I cannot wait!

I don't believe damping factor has been mentioned. Higher power amps tend to have a higher damping factor. With bass in particular, a higher damping factor provides better control of the driver and depending on the impedance of the speaker can result in more accurate reproduction.