Can single-sided Power meters cause unnatural Bilateral asymmetric pedaling? In case it is not clear for everyone, let me briefly explain the graph. The pink line represents the Power output along the y axis while the grey dots represent Left/Right balance in Power. The x axis represents time.

I was aiming for 360 watts in the beginning. Assuming I had a single-sided Power Meter (for my right leg) it would have showed smaller numbers where the Power Balance was more towards my left leg.

The direct consequence in holding a specific amount of watts using a single-sided Power Meter would be that as the Power Balance shifts away from the leg with the Power Meter, the total actual Power will go up while the numbers remain the same. As the Power Balance shifts towards the right leg total Power goes down.

The indirect consequence is the mind would subconsciously (or even consciously) learn to use the right leg more than the left leg. Especially in those crucial moments, like the last 15 seconds of an interval.

I'm looking for evidence to backup my claim. And since I am 100% certain that I am correct, why do people use single-sided Power Meters? Why do they exist at all?
I am unaware of any controlled study that directly addresses your question. 

However, a recently published study by Bini et al. addressed the converse of your question: can the provision of information on bilateral symmetry or asymmetry be used by riders to alter their pedaling dynamics? The Bini et al. study did not address whether riders would benefit from decreased bilateral asymmetry -- it only addressed the limited question of whether it was changeable. The answer appears to be that it can, sometimes. So although your exact question was not addressed, if these results are replicated and verified then a reasonable implication is that if one were to supply the riders with incorrect or misleading information on symmetry the riders might also be able to adjust their pedaling.