The cheese enchilada that comes with the Carne Asada is not really a cheese enchilada like is seen at Tex Mex eateries and probably not what you're thinking. It is only about 1/4 the size (and that's being generous) of the American version of the enchilada and it's designed to be an accompaniment to the rice and/or beans, not to be eaten straight on it's own as it's very spicy.
Sirloin Asado con Chilaquiles by
Tropical Wilds, on Flickr
The item on the top right, next to the beans, is the enchilada that they serve. I have a picture of the Carne Asada somewhere, but I can't find it, but the enchilada that comes with it is the same principle. The sauce is supposed to be a mopping sauce for the meat while the enchilada itself is eaten with the beans (usually) or the rice, and is eaten first. The idea is that the spicy sauce of the enchilada is tempered by the corn tortilla, cheese, and rice, but gets the juices going, as it were, for the steak. This is what the waiter explained to the table next to us when they complained that the cheese enchilada was too spicy to eat... He told us how it is supposed to be eaten and the customer went from being irritated, to understanding traditional Mexican cooking better.
Even when they offer/offered the vegetarian combo, the cheese enchilada was 1/4 (again, generous over estimate) the size of what people think are traditional enchiladas and it was, again, a mopping accompaniment for the beans.
Also, the Carne Asada is not one of their regular items, it is cycled in and out of the menu. When I was there in September 2011 they had it, but it was gone in January and replaced with something similar. The current, most up-to-date menu posted on the San Angel Inn website shows that it's currently not being offered as a regular menu item, though it may be a special from time to time.
http://sanangelinnusa.com/menus.html
In short, the cheese enchilada is not a meal item offered at San Angel Inn, and the cheese enchilada that is served there is not the Tex Mex, large rolled up bunch of cheese-packed tortillas. It's offered as an accompaniment, but not as a meal, where there's lots of sauce and only a little cheese as a binding and decoration on top. To ask for it as a meal, there wouldn't be enough of it to be satisfying and it'd be a significant deviation from the menu that, I think, would be difficult to accommodate and awkward to ask for. It'd be like going to 50's Prime Time and asking for just the vegetable and the mashed potato with a bowl of gravy instead of the meatloaf, or going to SciFi and asking for fries and vegetables but A1 instead of a burger. It's not how the dish was meant to be eaten and it will not be satisfying, not to mention a little embarrassing when it's presented to you.
As for other people ordering chicken tacos, etc off menu... I'm not sure you're thinking of the right place. At San Angel Inn, they don't even have traditional tacos, just fish tacos made with the seasonal catch. Even those aren't tacos in the American sense. They are smaller, made with slightly crisped flour tortillas, and topped with what most would consider odd taco toppings, like cabbage.
Fish Tacos by
Tropical Wilds, on Flickr
Maybe check out the La Hacienda, which has a more Tex Mex influenced menu and includes things like beef and chicken tacos. The food there is still Mexican, but it's toned down and slightly more Tex Mex traditional. It's less fine dining then San Angel Inn IMHO, but the Tex Mex cheese enchilada or American chicken taco isn't out of place there, whereas at San Angel Inn, which is aiming for a more fine dining meal, it would be very out-of-place.
I can't wait!!!!
