A “short squeeze” sounds innocuous enough...

Actually, what you said is not how it works at all. Most covered calls are in the end, handled by wall street dealers who hedge their deltas with short sales (trust me about this). Retail investors that do covered calls do own the stock, but the net effect is not what you described, it is significantly more complicated. (by the way, the transaction you describe is equivalent to selling a put)

Without closing out the short sales that were done, usually there is always unlimited downside to at least ONE player in this transaction. Why is this intuitive? Abstract for a second. Treat the short sale as a contract, which it is, where you agree that you have to buy some object back in the future in return for a FIXED dollar amount now. If you assume that object (a stock in this case) can go up to an arbitrarily high price, then you always have unlimited downside as long as this contract is in effect.

The point is even if you disallow these artificial short squeezes, you are STILL discouraging "stupid speculative bets", becuase the price can go up naturally (when the thesis of betting against the stock is economically wrong). These are the right times for it to happen, and in fact happens all the time without a volkswagen type squeeze. The point about short squeezes is that someone can make a "smart speculative bet" (which society as a whole needs people to do) but still get blown up for non economic reasons.

Effectively infinite risk? So you think a regulatory agency in the US will allow prices of a stock, say, GE to reach an unbounded number and still require settlement in derivative contracts to this? And I would not be as quick as you are in calling a professional stupid for doing something that any professor of finance would tell you is important for smooth functioning of capital markets.

You seem to just not grasp the magnitude of what you assume people should do in this crazy option proposal. It is not unusual for a stock to have a 25% short interest. That means a quarter of the shares are sold short. So you are saying a quarter of shareholders should sell calls to every short seller who wants to hedge? What if most shareholders do not want to sell options, and not give up the upside in doing so (indeed, there is a tradeoff in "juicing" your return, you lose the upside). In fact, most do not, so this is entirely impractical of course.

The whole point is with proper regulation that prevents the case of a squeeze or errant prices that are not sound, you prevent the "unlimited" downside (if a company ever becomes infinitely valuable, we will have other more interesting issues to deal with). This happens all the time--exchanges can cancel trades done at what are called "obvious error" prices. Regulation effectively clips the tail, which is why dealers have no problem shorting shares to ensure liquid markets.