The problem with ki is that it's a vague, mysterious word with no agreed-upon definition that is used to explain things that don't need explaining.
I'm not sure I agree. I can buy it being a mysterious word with loose definitions ("intelligence" comes to mind as another, perhaps lesser, example), but it's used to describe things that I think do need explaining, but the mystery of it is perhaps accepted too readily as an excuse to stop thinking about it.
Perhaps the ambiguity of the term is a little like "mind."
Whatever its relation to the physical body it is generally agreed that mind is that which enables a being to have subjective awareness and intentionality towards their environment, to perceive and respond to stimuli with some kind of agency, and to have a consciousness, including thinking and feeling.
Sounds like the brain to me. Clearly "mind" detracts from learning about brain function...except that it doesn't always; sometimes it provides a new lense which inspires new understanding.
If mind can be described as an amalgamation of certain neurological functions (which are not agreed upon within different schools of thought as to which ones comprise it), perhaps ki can be described as an amagamation of mind and body functions. So here we would have two terms used to loosely describe some sets of phenomina with no agreed-upon definition.
The example you gave of the guy moving kids with his ki seems rather dubious and reminicent of Dillman and his knockout punches that only work on his own students (i.e. classic conditioning). These don't disprove anything, of course. People do get knocked out all the time...I was knocked out a few minutes after I dislocated my patela (I'm a sissy though). That's an obvious example that "odd" knock-outs can exist, but perhaps ki isn't so obvious...kinda of like the potential varieties of Higgs-Boson particles (LHC = Large Hadron Collider...or possibly Left-Handed Corn, which is much tastier than Right-Handed Corn
When it comes to evidence-based approaches I'm not sure you can assert there is no flying spaghetti monster; all you can do is describe what model seems to help you understand phenomina the best and draw correlations. Asserting there is no Ki is the same as asserting there is no God: maybe; impossible to know given our current resources. I see assertions in either case as belief, not disbelief.