Because capitalism, supply and demand. If you give the common people more money, they will spend that money. This will cause the demand for goods and services to increase. To furnish this demand, employers will have to expand their workforce. And when unemployed people get more scarce, they'll have to increase wages beyond $15/hour to attract perspective employees. And this is what has happened every single time wages have been increased in recorded history.
You know what else happens when wages are increased? Corporate profits increase. With the possible exception of Walmart, every single business in existence has more customers than employees. This means that for every employee they're "forced" to pay more, they'll have several customers spending more money. The profit increase is seen as soon as a week after the wage increase.
Also to make sure corporations didn't even try the BS you suggested, I'd just write into the wage increase law that businesses are not allowed to engage in layoffs, hour cutting, or price gouging for a few months after the wage increase went into effect. If they wanted to offset the short lived loss of profits, I'd tell them to cut executive compensation.