That's a misunderstanding. When a company spends money to buy back shares, it decreases its value by the amount of money it spends. Therefore even though the company is now owned by fewer people, the value of the company has shrunk sinilarly, and the share prices remain constant. That is if the shares were priced correctly to begin with.
That is why stock buy-backs only make sense if the shares are priced too low.
No. The company decreases its current liquid assets, but a company's worth is not just assets, it's (liquid assets + value of ongoing profit). Assuming a fixed profit, a stock purchase would cause the profit-per-share to increase, so (assuming a fixed P/E ratio) the price of an individual share rises. Assuming the company buys the stock at a completely fair price, it's true that the company doesn't experience any change in value, but it has distributed money to shareholders - which just like distributing dividends except with less immediate tax implications.
(That said, I do understand companies usually overpay for their own stock, so the move is not necessarily the best one for any given company or companies in general unless the stock is, in fact, undervalued. But it is still one way to deliver returns into the pockets of shareholders, anyway.)
But the value of the company's future profits is already priced into the stock (provided the stock is priced correctly). Otherwise the value of the company would just be its book value.
If a company buys back stock that is overpriced, it actually destroys shareholder value. If the stock is priced correctly the outcome will be neutral for the shareholders. Only in the case where the stock is cheap relative to its value, is value created for the shareholders.
If this theory of share buybacks were true, it would lead to some fairly simple arbitrage strategies to make free money. (Buy shares in company x, force a share buyback so shares rise in value, profit).
In reality these corporate actions are value neutral if the current share price is at fair market value.
The value of ongoing profit is reduced if a company has fewer liquid assets to invest.
