Of course, the worker can choose to put a portion of their income into assets that generate income, and build wealth.
One's wealth has little relevance to the theory of worker exploitation, alienation and commodity fetishism. You can be a rich worker but still be exploited in the Marxian sense. You can be poor but still be an exploiter. One's wealth has little to do with the relationship to the means of production, unless that wealth comes in the form of private property upon which wage labour can be employed.
The fact is that "pulling up by the boostraps" is not an option for many people, and if it were it does little to stop systemic poverty, destitution and the need to sell labour-time very cheaply.
If a reader believes that the current system is the best system possible, than these politically-charged complaints sound as futile as politically-charged complaints about being unable to exceed the speed of light.
Managerial positions are of course kept (as managers are wage labourers too), the only difference is that there isn't someone at the top to collect surplus labour.
This is otherwise known as anarcho-Communism, or some variant of social anarchism. I am reading into communalism too (Bookchin) and the question of how those in service jobs can own their labour is an interesting one, I'm not aware of the current research on that.