My Breakfast Experiments™ aren't quite as rigorous as Mark Liberman's. He has direct access via a high-speed line to the entire Linguistic Data Consortium collection of corpora at his breakfast table, and writes R scripts for statistical analysis as if R was his native language (it may well be, come to think of it). My breakfast table has just a digital radio, a cereal bowl, and a mug bearing the legend "Keep calm and drink tea." But I'll give you some hard quantitative data for two different ways of expressing an affirmative response to a yes/no question or agreeing with a presented statement in contemporary British English. The frequency of people (especially experts) speaking to Radio 4 news programs saying "That's correct" falls in the monstrogacious to huge range (as measured by my casual early-morning impressions), while the frequency of that mode of affirmative responding in ordinary real-life conversation is roughly zero (source: vague memories of hearing people chat to each other). I hope that's rigorous enough for present purposes.
So why don't people speak to radio interviewers in a way that is at least something like the way they speak in other contexts? What can they possibly think is gained by saying "That's correct" rather than "Yes"?
Don't just type "That's correct!" in the comments box below (though I know you will). Tell me whether you've ever heard someone on the bus or in the workplace saying "That's correct" instead of "Yes". Do some counting. Me, I'm pouring another cup of tea. My work on this Breakfast Experiment™ is over.