Yes, you can restructure income tax levels so that people get to keep most of their additional income, and then you'd have to tax the remaining people more heavily to compensate. But if that's the solution, why don't we do that today?
This argument shows that UBI doesn't solve the incentive problem. It can only be solved by keeping welfare benefits significantly lower than minimum wages, which means lowering one or raising the other. This isn't logically impossible, but it's matter of political feasibility. That's true of UBI also.
I do think it's important to point out though that you lose unemployment if you work, so there's direct incentive there.
You stop getting the benefit if you get a job, you wouldn't stop getting UBI, so there's no negative response to being employed.
If UBI just replaces unemployment, how does that calculation change? You still have enough money to live on you still don't want to do the job being offered?
Unless UBI is sufficiently low that you need a job to survive, in which case... is it UBI?
A UBI that works as e.g. a negative income tax would definitely work.