One thing that does not seem to get factored in to free-market, water-flowing-down hill analogies is the different and lengthy time constants associated with some human changes, particularly with regard to relocation. Those different time constants can produce undesirable large temporary imbalances which may still last years or decades.
For example it seems to ignore the fact that while money flows freely and on a short time constant people, move much more slowly and most relocation options are not allowed by national governments.
So here is a thought experiment.
Let us imagine only one or a few spots on the surface of planet earth are the best for nurturing exciting employment. Let us say Silicon Valley, Cambridge, Bangalore, Hsinchu, Shanghai. There may be many more but the principle is that globalization seeks to create a polarizing effect that over time makes these hot spots available to wider range of people but to reduce the number of locations.
With increasing globalization and some freedom of travel it is possible that many many young people would become aware of and wish to emigrate to those places for the work. Only the best would be allowed to do so driving up land/house prices which could be afforded because that is where the work is. The average age in these regions would be younger and there would be additional work in these regions supporting these dynamic and well-paid workers. THIS ALL SEEMS GOOD.
Meanwhile the remaining parts of the world would be gradually empoverished, lose talent, have a higher than global average age of citizen, very many retired and sick people whose low incomes and low taxes would gradually cause the infrastructure to degrade and they would have fewer citizens of working age to service them. THIS IS BAD.
The argument that any and all should emigrate to one of the employment hot spots because that is where the work is, does not hold. The older members of society would not wish to, could not afford to, and would not be allowed to. It is close to saying "nature is cruel and devil take the hindmost."
We have seen similar social polarization effects on a national scale with key workers in health, teaching and other civil amenties being priced out of London and large parts of the rest of the UK becoming "sink" regions that are sustained by government spending of the taxes raised in the affluent regions.
However, that solution is not available on a global basis where there is no method to redirect funds.
The net result of such a free-market, pseudo free-movement strategy would be a polarization of global society both in terms of wealth and geography. Which is kind of what we already have!
The polarization of society is a consequence of globalization which, in turn, increases the rate of this polarization. The natural end point is not civilized and seems neither desirable nor sustainable.
This is more than enough reason for politiicians to step in. The question is then how much intervention is possible? And how much is advisable?
"Most people still live in countries with borders and citizens, who hope that they don't necessarily have to travel to another country to find work."
Heh. Why not? I did.
What I consider to be the "politicans' thinking" is what your second quote calls "citizen's point of view." In a global economy, it is becoming less and less realistic to expect that one can make a career where one grew up. Naturally, politicians will try to attract the right kind of jobs, too often in incompetent ways alas, but it's pretty hard to expect companies AND young aspiring professionals to think so narrowly.
""Globalization is like removing dams or other obstructions, that force the water level to be different in different locations.""
More often than not globalization is a nice management speak PR word for exploitation of labor or resources. In many cases it is in the interest of those describing their activities as golobalization to keep the dams of your analogy in place. Once the water levels are the same it is either time to move on, or in the case of employment bring the jobs back home.