commercial jobs are often explicit in the contract about the product and all derivatives being their property.
This. Most situations where your work would by used in any capacity beyond the buyer just acquiring the physical work, there would be a detailed contract.
Your initial statement made it kinda sound like just because it was for non-profit you should get it dirt cheap - sorry if I misunderstood - but this is the main point.
A private hobby person would just acquire the artwork for private use. The bigger the company, the more they would be using the artwork, hence the bigger price.
They always ask me the question: is it that for yourself or for the market?
Personally I hate this question because I am paying the talent and the time he will spent so as GK sayd he should not care about my purpose.
Artist shouldn't care what a private person does - but if the artwork is being used in any capacity other than you just owning the piece, it gets tricky.
I agree that the artist should indeed "simply" get paid for his time. But that's only the cost for him actually producing the artwork. From there you pay extra for everything beyond private use.
Also teeeeeeeeeeeeeeechnically you actually can't reproduce an acquired piece, even for private use, but who the hell is gonna stop you?

I don't think for an expert ilustrator it will take more than 2 hour to paint a HQ card in black and white,
Sounds about right
so if they will ask me more than 10 I will try to find someone else because I am doing it just for passion and will share with other people for free so I CAN'T really spend so much for it.
Your boss comes in and asks you to stay 2 hours extra - he offers you £10. BUT...! Your boss is very passionate about his business

At the end of the day you are asking another person to spend time doing work for you. It's as simple as that.