i dont know what protests you've been attending but the one's ive helped at for laundry and warehouse workers were filled with people that were not only supporting families on minimum wage but also contained people who were here on visas.
in america you're always taking a risk by protesting an employer.
This is, ultimately the major reason why the status quo never changes here: people dont want to acknowledge their class.
The ideal approach is two pronged, you raise the standard which benefits society as a whole and increase the social safety net to take care of those few lost in transition.
The same principle applies to a wide variety of economic changes from increased labor regulations, to housing, to free trade, to automation. Your complaint here is mainly that we haven't followed through on protecting those caught in transition. We shouldn't fall into the trap of mistaking that for a valid criticism against raising the societal standard.
I think the best way to increase wages is more and more jobs so that workers have bargaining power. I've used Uber as a fall-back and it dramatically increases my bargaining power.
I drove for Uber and it was seriously the only job I could get and it saved my life. I know of many other drivers who are battling disabling conditions who drive for Uber as well. Jobs that are as flexible as Uber are non-existent.
I find it really disappointing how many people debate this issue without ever actually listening to the people in poverty. That means talking to real people doing the job. Not just the protestors in the streets. And frankly, if you have time to protest, you're probably not that poor. The poorest of the poor work whenever they can and do not spend time on things that don't earn them money.