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Potatoes are a lot more expensive and more labor intensive to make than rice. Each one needing to be peeled is a huge time and labor sink. Whether it's done prior to shipping or at each location, it has to be paid for somewhere. You multiply that by hundreds of restaurants and thousands of employee salaries -- and there's your answer.
These massive chains consider everything when they add or remove a menu item due to the economy of scale. Cost of even $0.01 being the first one. The price of tomatoes going up or down a nickel is hugely important to Chipotle.
Not really unpopular, but definitely not thought through.  
Chipotle doesn’t change their menu on a whim and there is no benefit to them having potatoes on the menu.  They have their vegetarian options nailed down and the kitchen designed to cook exactly what they have on the menu.  Having to constantly cook potatoes and keep them warm and probably crispy (because that’s what I think most people would want is the “home fry style”) would not be beneficial.  
Please find someone who has refused to eat there because of no potatoes.  I doubt anyone has made that decision except for people who just want fries.  They likely never even consider Chipotle because they want fries.  Those people ruin menus.  Taco Bell is the perfect example.  Everything good there has been removed because of Taco Fries.  Worst decision ever for enjoyment and best decision ever for making money off of fast food vacuum people.