That’s not how income tax works, particularly for minimum wage workers.

It's just supply and demand. It makes working in these industries relatively more attractive, increasing supply of labour and therefore reducing price of labour. So restaurant owners capture some of the benefits

So employees earn more, and restaurants spend less. And this is bad because?

Well, the money doesn't appear with magic, so someone is paying: the government (forfeiting taxes) or the consumer (more pressure to tip).

To me, the bad part is the tax reductions only appear in behavior I don't agree with: high overtime and tipping (when it's semi mandatory).

I'm not American, but this is also showing up in my country.

Because you're artificially favouring one specific industry, at a cost to all other industries.

And because the implication of your argument is we should never tax anything because that's a benefit to both the consumer and the business

Aren't we already in a manufacturing hole and we're incentivizing more service industries over them?