This is just the flip side of why people support progressive taxes. If you believe that a flat tax is unfair because the people at the lower end of the spectrum have much less free money that isn't taken up by base needs, then it follows that different amounts of money affect people in different circumstances differently.

To the person with 10 million dollars, doubling their wealth is nice for them but likely won't result in a major change in lifestyle and what they could or couldn't do before. Maybe they go from a large house to a larger house. For the person that makes 30 thousand a year, doubling it makes a huge difference in how they live. The disposable income amount doesn't double, it's likely many many times higher, because it was such a relatively small portion before.

The same thing applies to one-time payments. It would make sense in your example even if the payout was much less (like $10k) but still affected the group similarly (i.e. if they had less disposable income). That amount of money is a huge to people that have little disposable income.