Why causing incomes to be equal is a good thing? Equal incomes for unequal work is a recipe for disaster, as those who do more valuable work would be discouraged from doing quality work if they can get the same for easier and less diligent one.
> If these assumptions hold, does that mean that pretty much any attempt at leveling the wage distribution within a capitalist system is destined to failure?
Yes. As much as one relies on voluntarist decrees to override the economic laws, it is destined to fail. Of course, the decrees would affect the wage distribution, at least for a time, and they may temporary improve income for some specific people, but ultimately since the labor price differentials are not product of absence of a decree banning them but of myriad of market conditions, these conditions would cause the prices to readjust or, if proper pricing is prohibited, to go to the gray or black market or be replaced. I.e. cheap fast food places may automate ordering and get rid of those minimal wage cashiers. Or hire just one instead of two and make them work more. Etc.
> i.e. negative income tax, basic income, etc. would also do nothing
Oh, those would definitely do something. Just maybe not the thing you expect them to do. If you institute basic income equal, say, to the salary of a teacher - which is not an easy job - then many people now employed as a teachers may choose to get the same money but instead pursue their leisure or some other less stressful activities. If you still need teachers, you'd have to offer them more to compensate them for giving up their leisure and endure the stress of the job.
Now, these extra money have to come from somewhere - so something has to be made more expensive. People that consume this something would try to keep their consumption level - if successful, they'd get raises too, if failing - they'd consume less, thus influencing those who produced that something and requiring them to be either compensated or find another employment. And so on, and so forth - the ripples are numerous.