I don't believe retail sales tax applies to tips in most (any?) states.

Why not? Why shouldn't sales tax or whatever tax also be fully paid for each received tip? It is not like other business gets to avoid taxes.

In principle: the money goes completely to the employee(s) being tipped, so it doesn’t make sense to tax the business for money it doesn’t receive.

Why should that matter? Let's say you run software consulting. And most of the price goes to labour. Would that not mean that sales tax should only be applied to part going to business itself?

Because sales tax is a tax on a sale, not on your employees' wages. Payroll and income tax (among others) apply to wages.

Whether payroll tax applies to tips depends on the municipality, but income tax always does.

You can't avoid taxes by not printing something.