The key to breaking this potential advantage is to let someone other than the coin flipper call heads or tails while the coin is in the air.

That’s how I was taught to do it as a kid when we were playing for fun. I never really thought about the reasoning until now.

If you talk to people deep into the performance magic community, there are myths and legends of people who practice dice rolling to the point where they can influence the outcome of a dice roll. I suppose training for hours a day for years on end could have some such influence.