More expensive = better?

All other things being equal, intuition would suggest that an amp costing $8,000 would be better than an amp that costs $5,000.

Keep it simple.  Its not like choosing Coke or Pepsi you know.

Assuming legit manufacturers, etc, a $150,000 preamp+amp(s) combo will always sound better than a $5000 integrated.

I would agree with this. Personally I don’t think you need to go up to $150k worth of preamp+power amp to beat a $5k integrated. A $50k pre power should show a $5k integrated a clean pair of heels. Having said that, to me, a quality integrated starts somewhere at $7k, new prices. The higher you go the better it sounds but one has to pick carefully, of course. Aspects such as preferences,  point of diminishing returns etc. will be applicable.

As mentioned earlier, some amps may be disguised to look $8k but sound like a $2k.

There are plenty of vintage amps available for less than $1K that sound as good as any of today's over-priced gear! I paid around $900 for a Perreaux 2150B - 340/680/920wpc @8/4/2 ohms. Sounds as good as any four/five figure amp!

IMO it will depend on what the higher price is for. Are you paying a higher price for one amp over another because there are higher quality components used? Are you paying a higher price for a proprietary design or circuit board? Are you paying a higher price for a better built product that brings tech support and help.

Or are you paying a higher price for an amp that is not built well with low cost components, off the shelf circuit boards. Are you paying more to cover marketing and advertising costs that add nothing to the sound. Are you paying more for an amp from a company that has to pay retail rent, heat, electric, and employees to sell them. Are you paying more for an amp that is sold by an independent dealer with a 200% mark up yo cover his business cost.

I would end with the answer to your question as being yes a more expensive amp can sound way better based on price if you are putting your money into areas that add to the sound not the fring costs that add nothing to the sound only to the cost.