Since nothing is said about what "transporter" means, I will assume it is something like in Star Trek, a sort of matter-to-energy conversion of the object/person to be transported, some sort of energy beam, and some sort of magical reconstruction of a living being at the sub-quantum level. Including, uh... the person's soul, or whatever.
The first obvious reason against using such a device in the middle of a battle would be that rapid movement, harsh manueuvers, nearby high-energy explosions and randomly interfering high-energy beams or electromagnetic pulses may not be what makes the process of transporting precisely safe. That doesn't even consider the possibility that a pirate would probably have a transporter scrambler. The Klingons do have them in Star Trek, sure enough.
Assuming a starship is operated by an antimatter reactor, the antimatter containment field would be designed to be the absolutely last thing to fail, for the rather obvious reason that a failed containment field is certain demise.
Which means at the time of the containment field rapidly failing, you will already have less vital systems (such as life support, shields, and... transporters) failed long ago. That's especially true for systems that consume a very non-neglegible amount of energy.
Assuming that shields are still intact, you would however still not be able to use a transporter because the whatever-it-is transporter beam cannot pass shields. How do I know it can't? Well, because if it could pass shields, pirates would rather take your valuable ship intact rather than shooting at it until it is at the point of disintegrating (doesn't make much sense if you want booty, eh?). They'd simply transport a hand grenade onto the bridge, killing the crew and leaving a mostly-intact ship.
That means in order to transport the crew off the ship, you necessarily have to lower whatever shields you have left. This means the ship will be torn to pieces by the next bolt/ray/torpedo hitting it.
Then of course, you are possibly within reach of a habitable planet, but quite possibly you are not. What do you do if there's no good place to transport the crew to?
Assuming there is a location where the crew can breathe and won't freeze to death within minutes, what do they eat during the next... let's be very optimistic, 3-6 weeks until help arrives? How would someone even know where to look for them?
A rescue pod addresses all these issues. It is devil-may-care autonomous, it has breathable air, there is some food and water as well as medical equipment, and is able to send a distress signal.