Whether any government mandated minimum wage boost "works", depends upon who you are. Who benefits from it?

If you are currently in a minimum wage job, you may benefit. You're making more money, because the government says so! (But your employer might just decide wage costs are too high and lay you off...)

If you are unemployed and looking for a minimum wage job, the bar just got raised. The higher the minimum wage is set, the harder employers look at how badly they need the work done. The job they might be willing to pay $10/hour for might not be worth $15/hour to them. Your quest to get a minimum wage job just got harder.

And if you are willing to accept less money, because some money is better than none, it doesn't help you, because employers aren't legally permitted to pay you less, even if you would be happy to accept it. So you likely get a substantial underground economy of "off the books" employees, getting paid in cash that doesn't get reported to the government. And those folks may actually take home more than minimum wage employees because taxes don't get deducted from their wages.

(I live in the NY metropolitan area. I see a lot of that. And there are employers who would pay the higher minimum wage, but the employees don't want to be on the books. Many are undocumented aliens, and being on the books leaves a trail pointing to them and possible deportation.)

If you are the government that mandated the higher minimum wage, you might not benefit financially, because the amount of taxes you see is less than what you might see if minimum wage was lower and more people had minimum wage jobs. (Of course, for government who do this, it's about getting votes, and impact on tax revenue isn't a consideration.)

And bear in mind that what the employee gets in a minimum wage job is rather less than what the employer has to spend. The employer must deduct and remit taxes, and must maintain the appropriate records for legal purposes, and that costs money.

Ultimately, "it takes two to tango". There must be workers looking for minimum wage jobs, and employers offering them. The government can't require employers to hire workers they don't need, and increases in minimum wage will tend to decrease the number of minimum wage jobs available.

Ultimately, minimum wage increases have the effect of decreasing total employment, but this seems to get missed in such discussions.

The goal of minimum wage increases is to insure workers can make a survivable income. But value is relative - something is worth what someone else is willing to pay for it, and that includes the worker's labor. Minimum wage jobs are minimum wage for a reason. They are low skilled/unskilled labor, and what the worker does simply isn't worth that much to those who need it done. What the minimum wage folks need is to be able to acquire the knowledge and skills that are worth more to employers and be able to get better jobs. Increases in minimum wage by themselves don't aid that.

We are seeing all sorts of commentary elsewhere about job losses to automation. The only reason many minimum wage jobs still exist is because it's more expensive up front to automate them than employers want to spend. At some point, minimum wage boosts might just make it worth the employer's while to spend the money needed to automate those jobs. Then what do the job seekers do?