The market cap is unambiguous, a more correct estimate of "how much to buy all the shares?" is situational and would just distract from getting the point across.

Not really. If a company were to manufacture a substantially large number of shares out of nothing (no additional investment money or other value entering the company) then the market cap would not go up. It would stay the same and per-share value would go down.

The market is mostly reasonable about who can and will sell their shares. If a big mover does sell a lot of their shares at once, the price will fall. Most big holders will slowly sell off shares for this reason.

In the other direction, it’s also understood that the cost to acquire all shares of a company is more than the market cap of a company. This is why you see acquisition prices being significantly higher than the last funding round valuation, or public shares popping on announcement of an acquisition attempt.