As you point out, this has a number of consequences, all of which are acceptable from the perspective of unions:
- Low wage unqualified jobs, beneath some lowest threshold of skill simply cannot exist. This level varies between markets, but e.g there are no shoe polishers or elevator attendants in Scandinavia.
- The natural rate of unemployment is higher than it otherwise would be. Basically instead of having 10% doing low paying jobs, you have 10% on generous unemployment benefits.
So essentially - and in accordance to all economic theory I know - having high wages and few unqualified jobs is certainly possible IF you
- spend lots of tax money on having an educated workforce
- have generous unemployment benefits
- Accept that society basically provides for anyone that doesn't provide value enough - either by training or just supporting them financially. Labor collectives prefer the state to pay these people instead of them driving wages down (because as you point out they don't provide that value)
Basically the scheme is possible if you tax the top N% of earners so much that you can let the bottom M% not have to work crap jobs.
Whether this is an appetizing solution depends on your political preferences of course, I'd say it's a pretty progressive version of social democracy, and it's found for example in the Nordic countries.
I don't think forcing companies to go out of business because they can't "provide wages" for employees makes sense. For one thing, that's not remotely the goal of the business. For another, nothing guarantees that these companies will go under, rather than (as most are doing) simply cutting back on some hours and some jobs.
You seem to suggest that the natural state of the world is a bunch of businesses paying a high wage, and that if we just get rid of all these businesses that are paying lower than that, we'd find jobs for everyone in higher-paying places. The truth is that some people simply can't provide more than $15 an hour in value to any business, for whatever reason, and no business will ever pay them more. These people will simply remain unemployed.