I've had the same thought and have built my system around the assumption this is true. I wish I knew.
I'm surprised that more attention isn't paid to this question, because it so plainly would inform how a person ought to spend their audio budget.
My speakers are far nicer than my other components, and I often wonder whether I would hear a difference if I upgraded my amp. My guess is maybe -- quite possibly not -- especially as I don't listen to a lot of power-hungry bass music.
FWIW, I run Revel F208s off of a relatively cheap AV amp (Onkyo TX-NR686, purportedly with 100 watts per channel (2 channels) at 8 ohms; 0.08% THD).
Signal source is Roon, with DSP filters set up using REW, using a $140 DAC (SMSL Sanskrit Mk2), a Raspberry Pi, and plain speaker wire. No sub engaged when listening to music. No room treatments other than furniture placement. The speakers are the highest-end component by a very wide margin.
So what do people think? Should the speakers be more than ten times the cost of the amp, assuming basic power needs are met?