What amount of share buy-backs are legitimate? My understanding of a shareholder buy-backs is the definition given by Investopedia:


  A stock buyback, also known as a "share repurchase", is a company's
  buying back its shares from the marketplace. You can think of a
  buyback as a company investing in itself, or using its cash to buy its
  own shares. The idea is simple: because a company can't act as its own
  shareholder, repurchased shares are absorbed by the company, and the
  number of outstanding shares on the market is reduced.


In "The Entrepreneurial State: Debunking Public vs. Private Sector Myths" by Dr. Mazzucato claims that shareholder buy-backs are a sign of stagnant economy that prioritizes stock prices and executive pay over things benefiting society:


  We are witnessing an increased financialization of the business
  sector, with many companies spending more on share buybacks—to boost
  their stock prices, stock options, and executive pay—than on areas
  like human capital and R&amp;D. As the work of Lazonick (2014) has shown,
  in the last decade, nearly $4 trillion has been spent on share
  buybacks by Fortune 500 companies.


I've reviewed the book if you're looking for more context to this quote.

Furthermore, Robert Reich believes they should be made illegal, as they were before 1982:

Stock buybacks are artificial efforts to interfere in the so-called “free market” to prop up stock prices. Because they create an artificial demand, they force stock prices above their natural level. With fewer shares in circulation, each remaining share is worth more.     


  Buybacks don’t create more or better jobs. Money spent on buybacks
  isn’t invested in new equipment, or research and development, or
  factories, or wages. It doesn’t build a company. Buybacks don’t grow
  the American economy.
  
  So why are buybacks so popular with Corporate CEOs?
  
  Because a bigger and bigger portion of CEO pay has been in stocks and
  stock options, rather than cash. So when share prices go up,
  executives reap a bonanza. The value of their pay from previous years
  also rises – in what amounts to a retroactive (and off the books) pay
  increase on top of their already outrageous compensation.


Is there some amount of shareholder buy-backs that could be seen as the sign of a healthy economy? Wherein "healthy" means still benefiting society via redistribution of wealth to those participating in the labour that created the profits or increase of collective human knowledge. Alternatively, what regulation has been proposed to correct short-sighted buy-backs?
If the company has excess cash or excess liquidity that it cannot effectively deploy in capital investments, and it has reason to believe that the expected value of returns from purchasing shares will be higher than alternatives (such as buying equities or financial instruments), this would be legitimate, where "legitimate" can be defined as an increase in the long-term value for anyone holding shares in the company.

As for determining how often this is done "legitimately", as opposed to being done manipulatively in order for inside traders to profit from reducing the supply of shares and thus illegitimately driving up prices, that's a different question. 

The question of whether it is "legitimate" in terms of share buybacks giving the executive board control out of proportion to shares held, this should be considered separately from the question of whether excess cash legitimizes the buyback from a long-term profit maximization perspective.

As for the question of whether excess cash that cannot be deployed effectively is a sign of a "healthy economy" or not, this need not be determined by the observation of excess cash of a specific corporation considering share buybacks. For example, one company may have excess cash that it cannot deploy effectively in a situation where it expects to earn higher returns from a share buyback than investing in alternative financial assets or securities, without this necessarily applying on an economy-wide basis (which would contradict a variety of theoretical assumptions about financial markets always efficiently reallocating capital to its most profitable use ... but that could happen.)

Relevant regulatory approaches to "illegitimate" share buybacks could fall under shareholder rights (other shareholders would be poorly represented by executives deciding on share buybacks to temporarily inflate share prices for their personal profit), or possibly in some cases insider trading. The regulatory framework, and its application, varies across jurisdictions.