That would be true for the absolute lowest value labor. Only about 1% of the labor force earned the minimum wage in 2019. Maybe that would increase to 3-5% under this scenario, with higher real wage compensation covering more people.
The competition for labor - which exists at all times in some form - will continue to force businesses beyond the floor of the income tax credit line for the extreme majority of labor. A person that now earns the minimum $12/hr via the tax credit system, a business can offer them $12 + their own $3 cost ($15/hr total to the employee), and steal them away for relatively inexpensively versus the old minimum wage costs. The business might have been paying a $10/hr min wage in their state previously, for example; so paying $3/hr for that labor is still a net savings. You could gradually eliminate the tax credit as you step up the income scale (maybe every combined dollar above $12/hr the person earns, one dollar in the credit vanishes; so someone earning $20/hr total, that employee loses $8/hr of the credit, so $16/hr of that has to come from the business; or half that rate of vanishing; you get the general idea). It's entirely plausibly this would massively boost income levels for the bottom half of workers, as businesses would offer over the $12/hr line to lure the best lower skill workers (it would still be net cheaper to the business than the old system, which is why they'd do it). It would also make a lot of small businesses solidly profitable and encourage higher rates of business formation again (most mom & pop businesses operate at very thin margins; would have to implement some new fraud checking and minimum revenue requirements perhaps; have to avoid various fraudulent employment schemes). Also, the credit should apply to lower income waiters also, they can keep tips on top of that (if they yield enough combined income, it would be taxed; a person earning the minimum $12/hr pays zero income taxes, over that we'd have to decide where income taxes begin and how they climb).
We would continue to tax normal corporate income outside of manufacturing (and we could begin by just experimenting by dropping manufacturing taxation to half the normal rate, test the outcomes it generates). The increased personal income taxation pays for the new redistribution model. We would want to reform our personal income tax system further to optimize, maximize it (including treating all income equally for tax purposes).
We could entirely exclude high wage employees from the income tax credit system, so those employees are not subsidized in this (if your engineers are making $125,000 they don't need the $12/hr income tax credit underneath them).
We simultaneously could alter some welfare benefit programs that are no longer as necessary as a larger share of the population is working and earning higher wages (you rebalance the system in other words).