Shareholders do not provide value, workers do. After he retired, Steve Ballmer did not provide $110B of value to Microsoft customers, but he received that wealth anyway.
That is completely untrue. Companies frequently own their own stock, and issue more when the price is high it continues to be quite valuable to the company
They can buy back shares and keep them in treasury, that's correct. But they need cash to buy them back first and it only actually results in a positive flow of money if they are able to sell it at a profit later.
And when they issue more, then this initial offering again (of new stock).