Earlier quoted context omitted.
What prevents shareholders from just selling their shares? Why does the company have to be the buyer? A company generating demand for its own stock does not create value, it creates liquidity. I hope you understand the difference. As for the solution, I think we're on the same page. Government debt should not be used for creating liquidity for shareholders holding a shitty asset.
Nothing prevents shareholders from selling shares. However, if a company does nothing - e.g. no growth, no buybacks, the future value of their stock will decline continually. through buybacks, they can hold those share prices steady, at least. This gives shareholders liquidity as you suggest - shareholders selling without buybacks means that they will push the price down. There's a line of thinking which says either…
Dividends seem also like the correct way to distribute profits back to shareholders. Buybacks on the other hand, I agree, are extremely shortsighted. If not used to go private and restructure the company, buybacks are a tool to provide liquidity to the more well-informed shareholders at the expense of other shareholders. Any sort of public debt financing of buybacks should be completely off the table.
Convertible debt seems like a good structure. If companies want to take the chance on the debt and they fail, the company would be effectively nationalized. In any case, a condition of any such note should be to prevent dividends and buy-backs. Any reasonable investor would probably include such terms.