Redoubling with three trumps

Why is that books and teachers tell us to redouble with a good hand and three of partner's major suit after RHO doubles?  What is the justification for this bit of nonsense?

The redouble should "imply no fit" and that means fewer than three major suit trumps.  How will partner be able to make a confident penalty double if he has a lurking suspicion that you might have three of his trumps?

Let's take an example. You hold ♠K84 ♥K7 ♦QT42 ♣QJ54, partner opens one heart and RHO doubles.  This is a clear redouble.  If partner has a decent spade holding (or if LHO bids a minor) we will double whatever they bid.  If LHO bids 1♠ and it comes back around, we can bid 1NT.

But what if we hold this similar but significantly different hand: ♠K84 ♥K97 ♦QT42 ♣QJ4?  If partner opens 1♥ and RHO doubles, we should pass.  Yes, pass!  We would normally bid a forcing 1NT and then jump in hearts.  So, in other words, we're willing to bid up to 3♥ without hearing of any extras that partner might hold.  If we pass now, and 3♥ is still available, we will bid it when it's next our turn.  Only if the bidding is already at the level of 3♠, will we be inconvenienced. In that case, we will double or bid NT according to the vulnerability.  Partner will know that we have exactly three hearts because we didn't redouble earlier and yet obviously have a good hand.  He will be very well placed to know what to do.

But I hear you saying "how will partner know we have a good hand when it's his second turn to bid?"  He won't.  But we'll enlighten him at our next turn.

Isn't it better for him to know your strength right away?  No.  It's much more important to tell partner about fit (or lack thereof) right away.  Strength can be shown later.

If you redouble holding two or three trumps, partner will know your strength right away but he still won't know what to do when your LHO jumps to 3♠.  He can't really double (penalty) with ♠Q5 ♥AQJ642 ♦K8 ♣AT5 because his spades aren't great and you might have three trumps.  But how can he bid 4♥ when you might have zero, one or two hearts?

So, does it seem odd to be passing with 10hcp opposite partner's opening?  Maybe, but the auction isn't over.  In the extremely rare event that they all pass, your partner will be playing 1♥X. That's not game, you say?  Indeed it isn't.  But let's see what our score will be if we can actually make 10 tricks?  Vulnerable, it will be 760 (like the sound of that?) and non-vulnerable, it will be 460 (not quite so good at IMPs but a very fine score at matchpoints).  But that isn't going to happen.  Someone is going to bid again, usually LHO.  If he passes, it means that the trumps are breaking 5-0 and this time you probably were never going to make ten tricks anyway.  But if you make your contract (perhaps with an overtrick) you're going to be well ahead.

BTW, since our redouble message now is only "no fit", we can actually do it with fewer than 10 points (if we compete later, we have at least 10).  But suppose we pick up this hand:  ♠KT84 ♥J752 ♦QT42 ♣4 and hear it go 1♣ double, aren't we likely to be better off in a different suit?  If LHO passes (he might because he might have long clubs), partner can bid another suit.  Our redouble has just performed double-duty as an S-O-S redouble.  If partner has decent clubs and no other suit, he can sit for it.  We probably shouldn't take this to extremes and do it with a complete Yarborough in case partner sits but can't make 1♣.  OTOH, if partner opens 1♠, and our hand is ♠4 ♥J752 ♦QT42 ♣KT84, we may already be in our best spot and LHO is very unlikely to pass it out anyway.