No, I don't think that's possible, novice_81, for the reason I gave earlier: it's tautologous.
If people would like to reduce suffering they would have to try and be kinder to each other would be fine (although I suspect the more usual construction would be If people would like to reduce suffering they will have to try and be kinder to each other.)
If people wanted to reduce suffering they would have to try and be kinder to each other would be equally fine.
Gramatically, "to want" is "would want" in the Conditional, so we have correct usage in theory. However semantically, conditional want is something of a paradox, which is why the clause sounds clumbsy at least.
Also phonetically, there is a dissonance in the juxtaposition of two words beginning with "w" which would be well avoided.
"Would" doesn't serve any purpose here; want is sufficient by itself (and the second "would" should be "will").
You can use "would want" in an unreal condition, an imaginary situation, or a possible situation that you do not expect to happen. For example: If you could be a character in a book, who would you want to be?
I can't think of a single political leader with whom I would want to spend five minutes.
The second example is a little more subtle. It is of course possible that one has a real existing desire to spend time with a political leader, and it might be possible to have the opportunity to do so. However, with "would want" there is an implied "if I actually had a desire" (I may not have thought about it) or "if I ever had the opportunity" (I don't think that I ever shall have), I would not want to.
One could also say: I can't think of a single political leader with whom I want to spend five minutes. but this is not "unreal" because it simply talks about one's actual desires.