No one in their right mind would consider 3 mm of clearance enough. That is borderline for a pure road bike!
A little bit of flex in wheel or frame, a wheel that is slighly out of true, and/or a little bit of dirt and your tire will easily eat away the carbon. And let's not talk about mud...
My alloy gravel bike is missing a good bit of paint on the chainstays after two seasons of autumn/winter rides, and that is with 5-6 mm of clearance both sides.
Really, the Specialized Tracer posted above is realistically already borderline. There is no "room to spare". If you want to use MTB-like tires, just buy a frame suitable for those.