Maybe. I doubt that many, if any at all will switch because of this. Legacy carriers cater to loyal/high mileage customers because they are their bread and butter and this guy wasn't picked to be removed because he is high up on the totem pole of frequent flyer status. While 1.6m miles is impressive, over 17 years that averages 94,000/yr and some change. There are customers who do that every few weeks with the airline. Those are the high value types they don't want to lose. I agree that anyone who purchases a ticket, no matter if it is Ma n' Pa Kettle on their first trip or Joe McFrequentFlyer on their millionth mile of the year, should be treated with dignity and respect but at the same time people need to understand that this isn't Nam. There are rules.
In fact, within the contract of carriage that United has, they spell out how they choose which passengers are to be removed and it includes both fare, and frequent flyer status among a smattering of other factors such as itinerary and when they checked in. As such, I would be quite surprised if this doctor was a frequent flyer and was picked to be removed over a leisure passenger who travels once or twice per year.