Hey, all we know about the Bird-of-Prey from "canon" is that it's a target for Captain Kirk!
What we saw on-screen:
1. It didn't have warp drive or at least they didn't use it, which is the same thing for dramatic purposes.
2. It only fired the plasma weapon, so that must be the only weapon on board.
3. It didn't even have a viewscreen, just those little viewers, I guess they were really on a budget that week...
4. It had atomic weapons, which when detonated a hundred meters from the Enterprise, did minimal damage.
5. And it only had a crew of about five.
6. It had a self-destruct system.
7. It had a cloaking device.
And from my degree in science, it would be tough to refit something with a singularity drive, unless you know how to temporarily shut down a black hole.
"Retreat?! Hell, we just got here!", annonymous American Marine, WWI
"Gravity is a harsh mistress....", The Tick