Baserunning and risk aversion (baseball stats puzzler)

When baserunners try to stretch a sure single into a double, how often are they successful?

I estimate the answer is: approximately 98% of the time.

The basis for this estimate:

Baseball-reference provides miscellaneous base running stats, including outs made at second that exclude caught stealing, pickoffs, and force plays.  These stats include being doubled off on a line drive, getting thrown out trying to advance on fly ball out, being thrown out trying to advance on a wild pitch or passed ball, and getting thrown out trying to stretch a hit (there are probably a few other things that end up getting classified in this category, such as getting thrown out in a run down after something other than a pickoff attempt).

In 2017, the average major league team made 15.7 outs in this fashion.  How many were baserunners trying to stretch a single into a double?  This has to be estimated, but I do happen to have stats on this more or less this same question for two teams, the 1984 Texas Rangers and the 1985 Seattle Mariners, and in both cases the percentage of these types of outs made that were actually runners trying to stretch a hit was 36%.*  (4 of 11 and 5 of 14 in the two cases respectively).

This suggests strongly that the answer to the question of how often hitters who try to reach second on a hit make it is very close to 98%.  (There were an average of 280 doubles per team in 2017, and 36% of 15.7 outs is 5.65 outs).

Now here’s the puzzler:  It’s generally accepted that the break even point for whether it makes sense to try to steal second is currently around 67%, typically, because the negative value of an out in this situation is normally about double the positive value of a stolen base (this will vary from team to team for various reasons, but it’s an OK rule of thumb for our purposes).  It seems to me that trying to stretch a single into a double is functionally identical to trying to steal second — in both cases the runner is safely at first but considering whether to risk acquiring another base against the risk of giving up an out.

Everyone would agree, I suppose, that a base stealer who was thrown out 2% of the time was being far too risk averse, and should be trying to steal far more often.  So why don’t runners try to stretch singles more often?

A related question: How should one analyze what the ideal level of risk-seeking for base running ought to be?  Should runners try to be aggressive enough to get at least close to the marginal point where the costs of aggression are balanced by the benefits, presumably around a 67% success rate?  Or is that not the right way to think about this?  In other words, what would be an optimal level of aggression among base runners?  While this would no doubt vary among individual players, surely a 98% success rate is far too high.

In any case, the extraordinary rarity of runners being thrown out trying to stretch hits does seem statistically anomalous, from a run-maximizing standpoint.

*I’m ignoring some hopefully trivially small number of potential confounders in the Texas and Seattle data, in the form of the possibility of runners being thrown out trying to stretch doubles into triples, or triples into home runs (In nearly 50 years of watching baseball I don’t think I’ve ever actually seen a runner thrown out at home trying to stretch a triple).