When the 3rd party of government tells a business owner that he must pay $1 extra to Sam, this is $1 the owner cannot spend and give to Bill, Mary, Sally, George, Harry, Susie....
When the 3rd party of government tells a business owner that he must increase entry level pay by $1, this is $1 the owner cannot invest in mid-level pay, senior-level pay, raw materials, construction, retirement, health care, infrastructure, advertising, supplies....
And, that business owner cannot reinvest that dollar in the business, to make the business grow, which would create more jobs. Lots of issues, as you note, are tied in with raising the minimum wage.