What you're saying is you want to bet a known house edge bet to try to lower the variance of another bet... That's the same as getting a 4 on the Don't Pass line, max odds, then throwing $10 on "hard 4" in craps... Goodbye money. "Thou shalt not hedge bets" - Wizard
But it's not really that simple. To quote James Grosjean in 42.08 "Contrary to what numerous authors have argued, insurance is not a side-bet independent of your main hand. Though usually negative-expectation, the insurance wager will indeed reduce overall variance on the player's \good" hands." It can make sense to insure good hands below the index as a measure to reduce risk. In some countries you can purchase insurance after you have resolved your hand but before the dealer has resolved theirs. So in these countries you can actually insure a hit to 21. So insuring 20 and 21 does make sense because you are maximizing your chance of being ahead at the end of the round. You might also abstain from insuring a sixteen right at the index to avoid the possibility of losing both the insurance wager and the hand. Keep in mind that right at the index the insurance wager is presumably break even or close to it so you are basically agnostic over whether you should make the play or not. It is the same principle as abstaining from doubling 9 v 7 at TC 3.2 because despite the fact that this play has marginally higher expected value it's really not worth the additional risk especially if you making a full kelly wager. So it's a little facile to say that expectation is the be all and end all of making decisions at the blackjack table. There are other considerations as well.
By taking measures to reduce variance, such as abstaining from excessively risky doubles where the gain in expectation is marginal (until of course the count is so high that the gain in ev is not marginal) and insuring good hands close to the index you can then bet more aggressively with less risk and end up making more money.
I'm trying yo follow this and get confused about "good hand". You're betting whether there's a 10 under the dealer's Ace. The "goodness" of your hand shouldn't matter, except that if it has one or two tens in it, it influences the odds of that undercard also being a 10. Otherwise, as May West noted... "goodness has nothing to do with it."
In fact, when discussing insurance with someone who DOES insure a "good hand" with no awareness of the count, I try to tell the guy that it's a side bet on the presence of an undercard 10, and that a "good hand" of twenty REDUCES that chance because it's used up two more of them.
OK - let the value of your hand go towards determining the true count, and take insurance when the math dictates it, but "goodness"? Absent bringing attention to my professional expertise, I'd insure my 16, or my 6, or... my 20... when the TC is +3 or greater. If I feel compelled to explain it on a "not good" hand, it's because at +3 I have 6 units out there, and "I get scared when I have a lot on the line,"
Do we sometimes over-think this business? The ancients analyzed this game for us, for years and years, and there have been no new numbers invented since someone thought up the "zero". The difficulty in the game is not having competing theories. It's being unemotional enough and focused enough to apply the elementary and simple ones we've been given in a hectic, sometimes hostile environment. That's where I screw up.