The more correct statement is "you never pay more in taxes by moving up a bracket" - though even that is not correct in all cases.

There are a lot of things (IETC for example, or benefits, or health insurance) which have $ cutoffs. Or tax breaks (i.e. electric vehicle credit) that only apply below a certain income. Exceeding those fixed points can certainly make you make less money.

One thing I ran into recently was fiscal incentives for homeownership (though not directly related to taxes) - there is a cutoff at a certain income level where if you stay below it you get a $10K credit towards closing costs. The tax code is full of things like that.

Taking into account only the federal income tax brackets, this is true. But tax cliffs exist, e.g. see: https://smartasset.com/financial-advisor/tax-cliff so accounting for all taxes and other factors, there could be a situation where you earn more pre-tax, but end up with less after all is accounted for. For most high-earners it's less relevant as they are past of the most cliffs anyway, but sometimes things like losing access to IRA deductions may be a factor too.