Firstly I would say, I think it's completely normal to have expressive body language when you play any instrument, including piano. For many people, or at least many styles - of music, emotional connection is a key part of playing and listening to music. You expect the performer to be experiencing an emotional connection to the music and to see that in their body language. I think you'd be hard pressed to find a 'professional pianist' that plays without that, in virtually any style. One particular youtube pianist 'scholar' does come to mind that plays like that and the effect is very dry - to me at least.
This really depends on what you mean by "expressive body language", and it's also a question of degree. Many/most of the pianists considered among the greatest played with very little excess motions of their arms or bodies. If you look at their faces you can see an emotional connection to the music but they also generally did not make extreme faces.
Among those who played with little extraneous body movements or extreme facial expressions I'd put Horowitz, Rubinstein, Rachmaninov, Hofmann, Richter, Gilels, Lupu, Kempff, Cliburn, Ashkenazy, Argerich, Arrau. Bolet, Hamelin, Hough, Sokolov, Barenboim, Gieseking, Cziffra, Lipatti, Kapell, Schiff,etc, Do you think any of those played with exaggerated motions or facial expressions?
It's only mostly in the last 20-30 or so years that some of the great performing pianists have shown lots of body or arm movements or extreme facial expressions. I can only think of a tiny number great pianists before that period that showed extreme body/arm movements(Gould) or facial expressions(Uchida, Serkin).
I'm not denying that the basically sedate stage presence of the pianists I listed might be in part due to their training. But, as far as classical pianists go, I can't agree with your comment that "I think you'd be hard pressed to find a 'professional pianist' that plays without that, in virtually any style."
Regarding the pianist you mention who plays with no body or facial expression, I think his quality of play is because he is far from a professional level pianist and not because of his restrained manner.
The pianists that play with these exaggerated flamboyant expressions do tend to get comments yes, but even they aren't really rare. If you watch someone play a beautiful romantic piece you fully expect them to be look like they're telling a poem to Juliet up a balcony, and if they're playing a blues or funk groove you expect them to be grimacing along with the beat like they're battling a toothache. That's just what we accept as normal.
I think pianists who play with exaggerated movements or facial expressions are more common today but still quite rare. I can only think of a few that fit that category that are considered at the highest level although, again, it's a question of degree. One person's idea of exaggerated movement could be another person's idea of reasonable restrained. If one sees just a typical conservatory student one may see more exaggerated movement that among the greatest of today's pianists.
In the age of YouTube, there are often extreme close ups of a performer's face with a view as if one was located directly in front of them and only a few feet away. From that close up a fairly high number of pianists can seem to have fairly extreme expressions, but I don't put that group if the "extreme' category because virtually no one in the audience would see what that close up camera view catches.