I don't know how else to say it, but abolishing the minimum wage would inevitably lead to many employers will cut the wages of their lowest-income employees. Is this really what you want? It's been proven time and time again that multi-national corporations will do anything at the expensive of others to maximize their bottom lines. If anything, the minimum wage needs to be raised (in many places, significantly raised) all across the nation. My rationale is, if a business cannot afford to pay all of their workers at least somewhat adequately, they shouldn't be in business adequately. And most businesses, both big and small, absolutely could afford fairer wages for their employes. The "it's bad for business" argument has been used against literally every workers' reform in US history, whether it be banning child labor, allowing unions, strikes, giving unions bargaining power, and pay equality for women and POC, yet last time I checked none of these reforms directly impaired the US economy.
You're not wrong when you say that higher minimum wages will likely result in outsourcing, which is precisely why so many different items are manufactured in Southeast Asia. And if every Southeastern Asian nation decided to mandate fair wages, than I suspect many, not all but many, businesses will move their operations to other poorly regulated places, like Africa. Even leftists like me are faced with this tough question. How do we ensure fair wages for all without having mass outsourcing? The government can't just force a business to stay in the United States, nor can it nationalize every industry.
And of course, the issue for many low-wage workers across the country is that they don't have a strong enough say in their wages. If a low-wage worker asks for a raise, it will most likely get denied. If they protest for one, they will most likely be fired, as low wage workers, in most sectors, are very replaceable. More than half of states across the country, even majority-blue states, have Right-to-Work laws which ban unions from collectively bargaining with their employers. This is why unions form and strikes break out. Yet CEOs and upper-level management can virtually decide their salaries on a whim. A way to aid this problem would be mandating that all corporate boards have at least ONE worker (ideally more than one though) present. Virtually all multi-national corporations do not have any actual workers on their boards. This was something that Bernie Sanders as well as other progressive politicians campaigned on.