I think reasonable people can disagree on this point, on whether not tipping constitutes a secondary exploitation.

No, they cannot. Disagreement here is not reasoned, it is just another example of clever people using their cleverness to justify unreasonable prior beliefs.

You can boycott a business, and write them to express that your boycott is based on their tipping policy. That would be a reasonable strategy to support the workers.

By still giving the business owners money, knowing they pay their staff sub-minimum wages based on the convention of tipping, and then not tipping, you have not communicated any disapproval to management. You have in fact directly supported the business owner exploiting their workers, and joined that exploitation for personal benefit. That’s the opposite of supporting the worker.