In a context of globalisation and high wage inequality, why should governments help unskilled workers?
After the exchange in comments, the OP appears to ask "why government intervention if the market will take care of the situation?"

Well we know that government intervention is advised when markets "fail" or, more accurately, are not characterized, at least to a respectable degree, by the ideal conditions required by theory in order for them to function efficiently.

But I will not discuss what could be the "market failures" in the specific case the OP discusses, and whether government intervention could actually improve things.  

Instead I will give an extra reason why in principle, government intervention may be required: the speed by which market forces operate. This matters a lot from a socio-political point of view, and it should also matter from a strict economic point of view, because, the slower the pace of adjustment, the longer the period of inefficiencies. So even if market forces will eventually tend to reduce the skills-and-wage gap, it is important how long it will take. And if it takes, say, decades, government intervention could in principle be argued in favor in order to speed up the process.