How do you deal with the fact that there are people willing to work for less?
So, at least here, your hypothesis does not seem to hold.
This is probably due to the unions educating those immigrant workers on what their rights are.
There are those that fit the professional association description, for instance the union of computer scientists which mandates a university degree in cs to become a member (this union does do collective bargaining with government and municipalities but not private enterprises), but then there are more broader unions for bigger sectors that do collective bargaining against the industrial collective (samtök atvinnulífsins).
So, I'm not sure what is with the downvotes for bbarn's comment. Its a point that isn't far off.
By having a collective bargaining agreement setting the minimum pay the company is allowed, leveling the playing field to remove exploitative measures like that.
That shouldn't happen, you need some morality in this amoral system so it can be less exploitative, one way to set some moral guidance is to have a minimum threshold of what people should be paid for a job given that others are already offered that for a similar skillset. Willing to work for less in exchange of other benefits (like moving to a different society) only creates cascading issues for the others who aren't in that desperate position, eroding the labour market.
If people were willing to be slaves, should we allow them?
(In addition: unions for employers exist as well.)
Your charge is nakedly hypocritical.
The answer in the Netherlands is that for most industries that have one the collective agreement has been declared universally binding. It applies to everyone in that industry, whether they're a member of one of the bargaining organizations or not, and if a company ignores it they're breaking the law.