I'm saying that it still doesn't make sense if you actually do the maths. A deflector dish which can absorb or deflect the sheer energy of a small stone packing megatons in kinetic energy, can also deal with the same megatons from a torpedo.
Really, as a rule of thumb, as Rick Robinson's First Law of Space Combat states, "An object impacting at 3 km/sec delivers kinetic energy equal to its mass in TNT." Over that speed, chemical explosives become superfluous, since just filling the warhead with lead or tungsten gives you more bang per buck than TNT.
Anything over 30 km/sec relative velocity, does weapons grade damage. Around 190 km/sec, anything does about the same damage per kilogram as a nuclear warhead.
And when talking relativistic speeds, 1 kg of just about anything travelling at 0.999c (which is still in the impulse region), delivers 454 Mt of sheer kinetic energy. Two kilograms are a bit over 0.9 Gigatons, or almost 20 Tsar Bombas (the biggest thermonuke EVER detonated) and you'll see in a jiffy why two kilos.
By way of comparison 1 kg of antimatter PLUS 1 kg matter, only gives you 43 megatons. And actually most of that will be, or soon (as in, within 10-20m even at high relativistic speeds) turn into, neutrinos which are lost energy. Once you compensate for that, inefficiencies, etc, sources smarter than me estimate you might actually get 3 megatons of actual deadly energy on the target.
Better yet, in the purely kinetic scenario, even the rocket frame, electronics, remaining fuel, EVERYTHING is extra destruction power, while in an antimatter+matter warhead, the actual explosive is much less. Out of a rocket of one ton, you'll have maybe those two kilos as actual antimatter warhead, so the amount added by the antimatter to the final damage is negligible. It's lost in the decimals.
Essentially at that speed, you just made antimatter warheads 100% obsolete and superfluous.
And the corrolary is also that a shield which can deal with a 2 pound stone coming at you at relativistic speeds, won't even break a sweat at a photon torpedo.
ETA: the other corrolary, of course, is that no matter how much antimater you carry, you're not going to do impulse 9, and also have enough energy left to stop afterwards, because every pound of your ship will pack more kinetic energy than you can get out of 1 pound of matter plus 1 pound of antimatter. And definitely not with a ship where 90% of it is ballroom-sized bedrooms, dozens of holodecks, whole families including children for every crew member (see TNG), etc. IF you can even do it at all, which I doubt, the sheer ratio between pounds moved to antimatter needed to move it, will make you more like a Saturn rocket, with a small ship at the front and a giant fuel storage behind it. You're not going to move something Enterprise sized unless you have something space-station sized with the antimatter to move it, and at that point any sane society will go, "you know what? screw it. The kids can stay at home and the crew can hotbunk. We'd rather have 10 battleships for half the cost in fuel alone, than one luxury cruiser for the officers." (And there'll always be SOME cost, even just in resources and manpower needed to make that stuff.) To return to economic sense, that is one thing in ST that just doesn't make any whatsoever.
Basically, I stand by what I was saying, the physics in SF don't make much sense either.
Yes, it's overthinking it, and yes, I know it's SF and not a physics textbook. I know it's role is just to illustrate some point via exotic props and species. But that's kinda my whole point: it uses whatever handwavium powered engines, and wishalloy hulls, and unobtanium warheads, it needs for that. There is no point in singling out one for not making economic or physics sense, because, really, the vast majority don't really make sense in either aspect if you actually start thinking too much about all the implications, a.k.a., start deconstructing it.
