Balky (big, over-sized etc) is used to describe people and objects, although a balky politician/professor/doctor/nurse would sound strange, as there is no standard size for a politician/professor/doctor/nurse.
It's a formation on "to balk" to refuse to comply. It means uncooperative, stubborn, awkward. So yes, it is appropriate to the types of people you list. It's not a word I have knowingly heard anyone use, but the meaning was immediately clear to me.
One would usually use the term "balky" to refer to a donkey or a horse. One might also say that someone "balked" at doing something , for example We made plans to go to a restaurant, but John balked at going when he learned he had to pay for his own meal.
In the game of baseball, the pitcher who starts to pitch must complete the action. If he stops without throwing the ball, he is said to "balk", and a runner is allowed to advance a base as a penalty to the pitcher.
Even with such uses, it would be very strange to refer to anything other than an animal (even a baseball pitcher) as "balky" -- that is, in the habit of balking.
I couldn't recall ever having heard this 'chiefly N. American' word, so I googled it.
Many of the links used the word to refer to a piece of computer gear or machinery that
'refused' to operate properly. There was also a mention or two of a piece of an athlete's
body, such as an ankle, that was acting up. I guess I might translate that to less colloquial
English as balky: does not operate as designed.
It sounds like the sort of thing headline writers would use, but not ordinary people.