And yes, buying and holding would slow down the market. A two to four week period would be about right, as a random guess, to eliminate predatory shorting, exploratory non-trades and pumping and dumping.

How exactly? The only thing a four week holding period would do is that the speculation tricks would begin four weeks later. Remember Henry Ford's great invention, the assembly line? It takes a long time to build one car, but if you start thousands in staggered intervals, then they come out the other end every couple of minutes. The same principle can apply to stocks with a holding period. An investor can still short a share, since he doesn't own it in the first place, he'll just borrow one from someone with an elapsed period. Pumping and dumping is a scam that works regardless of a holding period, etc. Finally, and perhaps most importantly, stock is only one type of security. Speculation is rife on all sorts of other contracts which wouldn't have a four week holding period.

And yet for some reason anything that happens on a stock market is supposed to be immune from legal oversight - why, exactly?

I never argued that, in fact I agree entirely with your sentiment. But we can't go back to a pre-computer world. In truth, the pre-computer stock market is no panacea either. For example, during the 1929 crash, the stock tickers were hours late in printing up-to-the-minute prices. Think of this as a crude form of holding period. Investors had the choice: act quickly with no clue at all of the current price, or wait some time to at least read the price of a few hours ago, and act too late anyway. A more serious problem with getting rid of computers is that the huge numbers of transactions would be curtailed, and accounted for by armies of clerks with pencil and paper.

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$E(X_t|F_s) = X_s,\quad t > s$