For me (I'm an aggressive player *), this is automatic. Minimum, but automatic. Even though they're not protected by being declarer, I like my Kings "over" opener's Aces (yes, I know the key is that one of them isn't this time. It will be more often than not). If you're going to reduce this by a point for being aceless, I get to upgrade it by a point for perfect shape (especially including both 4-card majors).
Will it always work? No. Yes, you are pinpointing your strength and more importantly your shape, if it turns out that you don't win the auction. But remember, if we do win the auction, they've pinpointed their strength just as much. And, since we have majors and they have diamonds, in the competitive auction - and most of the auctions are competitive auctions, not game auctions - we're in control.
I am not worried about partner going nuts. Mostly because we've had this discussion about what a takeout double looks like, and after he bids 2D "12+", I don't have to encourage. But also because a working 12 with a major fit, especially with DJxx(x) or worse (and partner will downgrade diamond honours, especially Q or K), will have a good play for game if partner insists on it. Kxx AQxx Jxx xxx has a play (not a great play - opener needs both black aces and only two clubs (or not a club lead), and the hearts need to split - but a play) and a hand that forces to game will have another king or ace, or much better shape.
But 90% of the time, especially at matchpoints, this is a competitive hand, and I would much rather explain our fit to partner before, rather than after, the opponents have passed their information. In response to "1D could easily have a 4 card major, and it might be our fit"; if they do, they almost certainly have a minimum balanced hand (assuming standard strong NT). Frankly, I'd be more worried about 4-1 the other way, with the points on my right and the trumps on my left.
- Edit: As an example, today I held at favourable A92 7 T872 K9762 in second, and dealer opened 1H. I thought about doubling, but finally decided that without 4 spades I shouldn't. The hand in the OP is better than that, even if aceless and without the spots.