Your first assertion has no bearing in reality. There's nothing prohibiting a closed-source API form being as fast as or faster than an open-source one. Your second assertion does not imply that your first is correct.

It may be that the current example of open-source are faster than the current example of closed-source, and there may be very real advantages that the open-source approach brings about that pushes the status quo towards as you describe, but there's nothing mandating that. I'm not sure why you'd therefore assert that.