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

Hello cclee2022.  If the power amp limits you, you will not hear the total advantage changing components might give you. So, some might say that if the power amp is not great, your system will not "sing."  Conversley, there is less difference among good power amps than there is between preamps and CD players. Power amps are more important than cabling. Pruifi's new amp modules, used by NAD and many others are superb.  I use two stereo pair daily. At least as good, and I think smoother on the top end, is the Starke Sound A4-320, I have three of them. They are simply stunning. Home trials are allowed. Check their website. Last year, they put them on a "Black Friday" special. If they do it again, I will order two more. At the regular price (under $1500 last time I checked), they are the best bargain since the Magnepan LRS. On sale they are a no-brainer. I used to build my own power amps, not any more! I use electronic crossovers from miniDSP and DBX. Get the passive crossovers out of the amp/speaker path. You will be suprised! Most power amps have the ability to control the motion of the actual driver diaphragms ("dampong factor"). Coils and capcitors interfere with that. Also, the speaker cables are much less fussy when connecting the amp directly to the voice coils in the drivers. Are you "handy" with tools and small parts? Try the kits from Akitika. Happy listening!

What influences the sound characer the most, in order of magnitude:

1. Speakers
2. ROOM ACOUSTICS (often forgotten)
3. Amplifier
4. Source (CD player, streamer, DAC)
5. Cables

I'd spend my money in that order.

SQ is not proportionatel to expenditure.  Allocating expenditure by percentage is not likely to give you the best bang for the buck.  Pick components whose sound you really like.  Be prepared to dive in deeper if required and spend less on other areas where you don't discover a stand-out for you.

That said, I mainly agree with Pani.  Transducers are the area that influences SQ the most, that is record players, digital players and speakers.  Money spent there will have the most effect.  Then look at amplifiers.  For some, room treatment is a must, but it is best not to listen in compromised rooms, some of which remain compromised however much is spent.  Wiring comes last.  Whatever Miller says, it cannot influence SQ to the extent active components do.

Foolishly, Miller advocates equal expenditure on room treatment and wires.  That means you only spend 16.67% on players and on speakers, when if you were more sensible it would be 25%,  That's a stonking 50% uplift.

If I had to decide in the restrictive manner proposed by OP (and did not have a compromised room) I would go:
30% speakers, 25% player, 35% all amplification (less if you go integrated), 5% room, 5% wires.  And that's generous on the room and wires.

If you are digital believer and only run digital, I would drop expenditure sharply on the player (incl DAC).  True converts know that if you have sorted jitter, clock error and have a good DAC, bits is bits, so any decent player will do.  Read errors are almost non-existent on every player.

The strongest part of any system is it’s weakest link. …or something along those lines

50% gear/cables, 50% room treatment and speaker/listening position placement.

That is not COST, it is the importance and true perspective of a TOTAL system.

The cost of gear and cables can be 100% of the cost, but it's still only 50% of the sound. By putting 5-10% ($$) in room treatment you can reduce your gear cost buy 50-75%. The sound can cost a lot of money or VERY well spent money. The well spent money part, usually comes with a lot of poorly spent (learning) money through the years. :-)

I look at it like this TOO.. 300hz and down gets a certain kind of control system (bass control system) fed from an active preamp (integrated or separate), power amp (class Ds), cables and speakers.

300 hz and up gets a very well made versatile valve power amp for 8 months out of the year and class ds for the HOT summers where I live.

When I was finished with one system I was still under 10k and everything was new or freshly gone through and or moded up.. Room included. The front room my wife's system.

I could add in 15K speakers that I have, but the 1500.00 speakers with the brand new cabinets I purchased for 200.00, work as good because of the room size and type of speaker. I could add a 8K preamp I have but the C20 that cost me 1700.00 total with a complete rebuild, and on and on and on....

The NUGGET from all this is:
I can build a 60K system or a 8K system. I have both... 50% is still the room.. at 5-15% of 8K. LOL :-)

ROOM first, speakers second. I'm sorry I work backward than most people. Then the power amp matches the speaker and the room temp issues.. It's a BIG issue where I live..

Source is source pick what ever you like for your Karaoke Christmas hootenanny. :-)

Regards