Inflation is unstoppable and the only way to deal with it for most of the people is to have more purchasing power and one way of having more is through increased minimum wage.
This is not right, the effect is the opposite of what you describe. Increasing minimum wage increases the purchasing power only temporarily, then causes even more inflation and the situation is back to the beginning or even worse than where it started.
For all to benefit with the raise, the government needs to adjust as well their taxation to these businesses and give incentive so that they can comply to the increase of wages.
Minimum wage is not done with incentives, it is mandatory by law. A business has no choice but to accept it, any employment that has a salary less than minimum wage is illegal.
The idea in general is flawed because it ignores the major factors in job creation. I believe in a bare minimum setting for wages, mostly so people dont get treated like slaves which surprisingly still can happen hence it formalises the felony conditions of exploitation mostly.
The confusion comes from forcing any wage or price to be true, in a free-market economy this is failure from day one. The cost of labor is a commodity or input cost to a business, and it can force the business to not exist if the wage were set too high. So min wage can destroy jobs, reduce opportunity and raise unemployment, its an ironic effect that follows over governance as has been proven countless times.
If government wants to create an absolute barrier and its far above the lows, gov must pay the difference to ensure no restriction occurs to business. It can't be another tax on jobs, in some cases a business automates the jobs using machines or exports the labor process abroad to ensure a low cost of labor. Force most often fails, gov can subsidize a final wage in some way and control the budget itself in that way.
That is correct, this is a death sentence in free-market economy but it seems that many still believe in these kinds of ideas. I guess this is one of the reasons why life has been getting worse and worse for the middle class in the recent decades in the most developed countries. They continue to adopt some ideas every now and then that makes them less competitive and that cause negative friction in a free-market economy. We need actual solutions that handle the issue long-term, and not ideas that are like short term band aids and that come back even worse after some time..