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Depending on the tax system that is an actual issue.
At least in the US there is no possible situation where you'd get less money for making more money.
I don't believe that's actually true. I think in the USA there are a few programs that have a hard cap on income to disqualify you. Food and housing assistance related things. I'm not American so I'm not 100% sure on them but I do think there are some scenarios
That's true. You'll still be making more money, but you'll also have more expenses. This doesn't apply to most people though, and for sure not ones getting a $10k raise. The progressive tax system we have only applies the tax as you progress through the levels. The first $10k will be taxed at one level, then the next bracket, then the next, etc. It's not done as one lump tax.
Different programs should be set up to slowly decrease how much you get instead of cutoff amounts. That'd remove that issue. Obviously some things are either on or off so they can't be done this way though. Ideally a lot of it should just be provided to everyone no matter what though.