Not necessarily (think about it!), but in any event, it is far from clear that minimum wage actually gives more people more money.
Counter examples (actual, real-life, counter-examples supported by data) would be interesting to read.
You can, of course, add the money received by those people who benefit from the minimum wage laws to the total money available to spend. However, businesses pass increased costs on to consumers, or go out of business.
Or they could, shock, horror, take less in profit.
In effect, people's net purchasing power goes down. Instead of helping the people you want to help, you end up hurting them.
Purchasing power isn't going down because labour is getting more expensive, it's going down because labour is steadily getting paid less and less because capital is taking more and more.
The only place the continual downward pressure on wages ends is a tiny proportion of wealthy people who own everything and a huge proportion of people of subsistence incomes. When hardly anyone has any disposable income, where do you think economic activity is going to happen ?
Thus, merely "increasing" economic activity is not a valid goal: to be beneficial to society the economic activity has to be healthy activity, not the production of shoddy products. This can only be the case if we don't cause a net reduction in people's buying power (which is what minimum wage laws tend to do).
Again, evidence to support this claim would be useful.
In reality, countries with higher incomes at the lower-end, rather than the rock-bottom incomes you are advocating, are the countries that have the higher quality goods you are insisting they will not.
No this is done by welfare laws (of which there are a plethora).
No, welfare is there as a safety net for people who are unable to work. Since neoliberalism took over the western world and maintaining a certain level of unemployment became a policy goal (to reduce worker bargaining power and suppress their wages), it has become a necessity for millions of people ready, able and willing to work but who cannot find anyone to work for.
What you are talking about is a universal basic income, which would need to be set at a similar level to minimum wage to meet that objective.