You make a good point, but then, JFK was still progressive on many issues, and still had close ties to, and relied upon organised Labor for support. He even paid lip service to European-style universal healthcare.
“The fact of the matter is that what we are now talking about doing, most of the countries of Europe did years ago. The British did it 30 years ago. We are behind every country, pretty nearly, in Europe, in this matter of medical care for our citizens.” — JFK, NYC, 20 May 1962