OK so in this case how do you set the price? Based on the final solution to be delivered? Can you give one (or a few) concrete examples by any chance?

I am not sure if I fully understood what you meant exactly with your (detailed) reply.

You judge how valuable the solution is to your customer and then structure your pricing to maximize your profits while still being palatable to your client.

Let's say your client has a problem that will bring them 1k/hr of revenue when fixed. You think you can fix it in an hour.

You could quote them 5k/hour, because you think you can fix it in one hour and you estimate it'll take them at least 5 hours to find and talk to someone else who could fix it. This is a big gamble for the client, what if you don't fix it or take longer? The client balks.

Now let's say you offer a "reasonable" hourly rate like 150/hr. Your client is happy to take the gamble because 150 is peanuts compared to the value they get if you do fix it. Client takes the deal, you fix the problem, but you got paid peanuts.

Now let's say you offer them a no-fix-no-fee rate of 5k. The client is happy to take it because once the problem is solved it takes them just 5 hours to go back in profit, and they risk nothing if you end up not solving the problem. They take the deal, you fix it in an hour, the client happily pays you 5k, netting an hourly rate of 5k/hour.

Same hourly rate as the first scenario, yet the first scenario will cause everyone to balk while the second one is a steal for the client (in reality, you can actually charge more than 5k, how much more depends on your reputation and sales skills).

I read it as:

“This is the price for me to do work I don’t want to do, but will do, if you make it impossible for me to say no.”

It’s not about justifying the rate, that’s the wrong way to think of it.

"You make $100, you pay me $20, I make pho you"