You're absolutely correct regarding tips being a "subsidy for the business". The reason "tipped minimum wage" (where it exists) is lower than actual minimum wage is because the business claims a "tip credit" towards meeting their minimum wage obligation. They're essentially telling the government "this person will make up the difference (or more) in tips, and that will meet our legal obligation to pay the minimum wage."

In most jurisdictions, this is figured by taking the employee's wages plus reported tips for each pay period and dividing them by the employee's clocked hours for that pay period. If that result is not at least actual minimum wage, the employer normally owes the employee the difference.

I don't know if it's a lack of knowledge or actual malicious pay practices (probably some of both), but number of people I meet in the service industry who don't know that last bit and tell me they've never been paid the difference for "dead" shifts (those that generate little to no tips) is staggering.