Impulse engines are probably too large and expensive to put on something like that, and you might need big starship-grade ones to be able to get something moving that quickly.
You would also want a tough deflector system, so that it isn't immediately obliterated by the first piece of space dust that it runs into, and a nice computer so that it doesn't just fly off into the first star 'til morning, and at that point, it might just be too expensive to bother with. You're basically building a small starship at that point.
One argument I tend to see when this comes up is, that the shields would block it. Which then makes you think, if they could block that, then what couldn’t they block? It makes them pretty much invincible. So I don’t think that’s it.
At least in Trek, 24th century shields are extremely good at handling physical impacts. Even in a compromised state, with one of the shield processors having escaped and gone rogue, an ageing California class was able to take several hard impacts without so much as a scratch. They might have been able to resist indefinitely if their shields were performing optimally.
Earlier ones, like the ones fitted to the Kelvin-era Enterprise, are much weaker against physical impacts, such that the wreckage of a starship was able to still cause major damage to the outer hull, even with shields at full.
Shields are probably much weaker against energy fire, since they appear to be an outcropping of deflector screen technology, and as such, fare better against physical objects. A powerful energy weapon probably does a much better job at knocking down shields than just smacking them with the physical photon torpedo, even if the torpedo is fired at warp speeds.