It's because it's easy and administratively simple, and it's easy to figure out how much you have to earn before you can actually bear the cost. In reality, it leads to a grey area where in the short term you're better off earning less to get the benefit, but it's eminently fair and easy.
And in general, increasing taxes is not easy, and the richer people are, the more able they are to fight against it. So we often create regressive tax regimes despite knowing they aren't very good systems.
First off, the following is not meant to combative but I think this confuses me. If there was no cliff there was nothing to do administratively on that front, no new checking at all. We already have progressive tax systems in many countries. Adding 1% at the top end can’t be that difficult. My health insurance (in Germany) raises prices every year and most people don’t have a choice there either. Property taxes increase all the time. If we had a wealth tax and a higher (at the top) progressive capital gains tax it seems to me that the pitch would be politically even simpler: there are 5% that will pay a little more percentage wise from now on while retaining vast amounts of wealth and 95% that will pay less or much less. Genuinely I have heard that we can’t raise taxes on rich people because they will evade them but it also sounds like a lie repeated so often that we just take it as the truth. Didn’t a lot of countries or US states have higher marginal tax rates without seeing mass exodus of millionaires? Can’t lawmakers focus on plugging the loopholes rich people use? I mean our government is currently trying to go out of its way to make sure that unemployment benefits are only paid out to people who „really deserve them“ by tightening the rules around that and the political debates I see put incredible amounts of emphasis on „fairness“ and that we „have to do something about those who just profit off the system without contributing“ when it’s about that topic. The fervour is clearly not applied symmetrically.
It’s easy to understand, but not easy to live under. If the worst case is I lose 25% of every “extra” dollar in some range, I have to think about it way less than if I lose the entire benefit for being 1 unit of currency over a limit.
In the former case, I can think/worry about it for 10 minutes per year; in the latter case, if I’m close I have to think/worry about it a lot more and carefully plan out and estimate things like tax-deferred savings and capital gains/dividends/capital gains distributions to make sure I don’t earn an extra dollar and pay $10-25K of marginal tax on that dollar.