My guess is that the column's transporter main circuits adds or subtracts energy (the ionizer) to the transportee's stream by using the main engines as a buffer/reservoir.
If there isn't enough power to do so or not enough capacity to absorb the extra energy then the abort control circuit would safely prevent the transporter from accidentally scrambling the transportee on arrival.
I derived this guess from Scotty's solution to run circuits to the impulse engines to perform the same task. I suppose for whatever reason, it would have taken too long to run the bypass to the main engines (or too dangerous without an abort circuit that can handle the main engines extra power)...
SCOTT: Mister Scott, sir, on the lower level of the Engineering deck. I've found a new trouble with the transporter. The casing has a wide gap ripped in it. The main circuits have been burned through. The abort control circuit is gone altogether
KIRK: That unit, Scotty, status report.
SCOTT: The transporter unit ionizer. Nothing much left of it, sir.
KIRK: How bad is it?
SCOTT: We can't repair it in less than a week.
SCOTT: We've found a way to get the transporter working, sir.
SPOCK: We've attached some bypass and leader circuits to compensate for the difference. Tied directly into the impulse engines, there shouldn't be more than a five point variation in the velocity balance. I suggest we send the animal through.