In a context of globalisation and high wage inequality, why should governments help unskilled workers? With globalisation, wage inequality continues to be a strong issue for many developed nations.

What I seek to find out here is, why should we even do anything to help the unskilled workers?

From what I understand, having minimum wage laws and various skills training policies are put in place to help the unskilled. However, we should know that unskilled workers generally do not know economics. The main issue they are having is that they know the "poor is getting poorer, while the rich is getting richer." Given that, they do not understand that unskilled workers are gaining less from trade in comparison to skilled workers, and therefore are not helping themselves to "upgrade" and join the skilled force labour. 

I know that there are countless manual, unskilled labour required and if the whole labour force is skilled, some would have to be forced into unskilled labour jobs. However when our society can reach that point in time, I assume the the wages of the unskilled labour would have also increased to a point where the wage gap is insignificant enough to draw some of the labour force towards unskilled jobs. But this is only possible if the country is closed off to foreign labour.

As a developed country, most of the labour force are already skilled workers. The reason why wages of the unskilled labour have not increased, in my opinion, is due to foreign labour. Labour from emerging markets i.e. China/Myanmar/Phillipines etc. are suppressing the wage growth of the unskilled labour force.

So as long as there are countries with large labour force that are "under-developed", wouldn't that mean no matter how much you try to help the unskilled workers, the influx of unskilled labour from emerging market eventually wipes those efforts away.

On the other hand, if we do nothing to help, the growth of an emerging market eventually catches up to that of a developed nation as growth plateaus progressively. We eventually reach a point in time where there are no longer any "undeveloped" countries. The unskilled foreign labour would much rather work in their respective countries then and the resultant would be more unskilled workers becoming skilled which increases wages for unskilled jobs, pulling wage inequality together.

What am I misunderstanding here?
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.