Notice that this distinction is entirely social and psychological and has nothing to do with the actual micro-economic incentives that apply at various levels of class status or wealth. You describe how poorer people get more value per marginal dollar added. While this means that a commitment device that uses money costs more in practical value. However, the same consideration applies to the motivational impact of any given monetary incentive.

Diminishing marginal utility applies to both sides.

It's more complicated than that. As explained in Thinking: Fast and Slow, most people are risk adverse in gains, risk prone in losses, and weigh losses more heavily for gains, but whereas for well-off people gains and losses are measured from the status quo, for the very poor they're counted from a higher level, so that up to a certain point getting more money feels more like a reduced loss than a gain (which is why poor people are more likely to spend sizeable chunks of money on lotteries).

So, it's well possible that the risk of losing 1% of one's money has a different motivational effect for someone very poor than for someone well off.