How much does power amplifier really matter comparing to other hi-fi components?

Everything matters especially amp and preamp.

Depends on the loudspeaker. If you have something really efficient, a nice pair of Quicksilver monos will do the job. But if you have Magnepan 20s, the sky is the limit. 

Matching amps to speakers is a critical consideration. Depending on the 1. CD player / DAC and the 3. Power-amp compatibility;  the 2. Pre-amp might be superfluous.

It’s hard to say. It really depends on the chain

In a recent video series Jay compared a rogue audio class D amp to a high end amp. I dont remember if it was duel mono or not because he didnt specify the elite amp, but for sure it was over $30k vs an amp less than $2k.
While differences were there, they wernt profound and many couldnt even tell the difference

My point is, Jay’s chain is unreal. Hes using power cords that are more expensive than most peoples entire hifi setups. In addition he has 2x Everest power conditioners as well as Synergistics top of the line conditioner. Then add to it the pre amp, the super high end interconnects, his very substantial electric setup behind the wall, ext..
All of this helped to make up for many of the cheap amps inadequacies as well as color the sound and change the sound signature.

If you were to take the same amps in a more modest setup I’m sure you would hear a much bigger difference between the amps

So to sum up a lot of it depends on the rest of the chain. In a mega high end setup the amps impact is much more minimal as long as the power and current capability is there.

In a more modest setup the amp choice will matter much more.

i think the 20-25% figure is fair

As for the pre-amp, this is also difficult to put a value on. some ppl with higher end DCS or even something like the lumin x1 choose to skip the pre-amp all together and go straight to amp.

Others will find that the pre-amp is the 'heart" of their system and actually put #1 cost priority to their pre.

I think you should make a decision on the speakers which will be the most important/influential and from there it will be much easier to assign values.
If you were, for instance, to enjoy horn speakers and were to go after something like klipsch higher end stuff then you would find that you can save a lot on the amp because so much less power is needed to run something so efficient. 
On the flipside if your flavor was something more like high end magico you would find that the amp choice is very important and you would need to allocate significantly higher percentage of $ to the amp 

So really it starts with the speakers, from there you can start assigning values to the remainder of the chain