I've believed for a long time that breaking ability has more effect on the outcome of a game than it ought to have. It should of course be rewarded, just less so in my view personal view. Therefore I would like to see a narrowing of the box from which you are allowed to break in the first place, including complete removal of any possibility to break from near either of the side rails. The better breaker would still be rewarded, just to a lesser comparative degree. This is one of the things I think IPT got just about right.
To get back closer to the topic, I think that the biggest factor in achieving a controlled effective consistent break is your 'comfort' factor with the shot you are trying to play. If when breaking you genuinely think you achieve a better stroke and results from the left side rail, you probably will stroke it better from that side and the results will automatically follow.
Although I don't know exactly what they are or how they arise I think we all have factors in our physical make up, other than simply whether we are right or left handed, which affect our 'comfort' zones in directional terms. For example, I am pro golf standard right handed and was a right footed soccer and rugby kicker to a good standard. However, contrary to what might be expected from that I am greatly more comfortable when diving to my left to try and catch a football or cricket ball than when diving to my right and cannot even think about leading with my right leg when jumping a hurdle or a fence, it has to be left.
In respect of more practical and technical stroke mechanics, the comfort factor in breaking from right or left side rail may also be partly affected to differing degrees by your preferred style of bridging due to the different potential positions of your bridge hand relative to the rail and the table bed.
I think that most right or left handed people would say that that they do have a preferred side rail to break from but that they are not actually entirely sure exactly why they receive better results from that side and I think this backs up the general 'comfort' factor argument rather than anything too technical.
One side rail may well transpire be a significantly more favoured breaking choice by right handers and left handers respectively, just as most right handers are more comfortable cutting balls into pockets in a right to left direction rather than in the other, whereas left handers of course prefer the opposite. Right handed golfers in general find right to left putts a lot easier to hole than left to right.