A good bit of it is that it is the only restaurant around the World Showcase that serves food that non-adventurous American diners would enjoy.
I'm not sure I totally agree with this.
In terms of table service (I'm not going to include Biergarten, since it is a buffet style - even though most of the food there isn't terribly "adventerous"), there are a few options for non-adventerous eaters.
I will also exclude Bistro de Paris, since it has the added dress code an no children's menu.
Effectively, that leaves you with Le Cellier, Rose & Crown Dining Room and - I would argue - Chefs de France.
Main dinner items at R&C include:
Harry Ramsden's Famous Fish and Chips - Batter-fried fresh Cod served with English chips and Garden peas. (Fish and Chips are pretty standard fare)
Pot Roast - Sunday dinner-style braised beef with roasted veggies, mashed potatoes, and Red Wine gravy. (Unless you dislike red wine - this sounds like something served for an American or British Sunday family dinner)
Admittedly, the other dishes include some different sauces - like a mustard sauce on the pork loin, and the steak and fish has a black and tan sauce (made from two beers - Guinness and another ale - although many argue over which ale is the correct one)
Not as much choice of "non-adventerous" food compared to LC, but at least a couple of rather standard dishes
In terms of Chefs de France - I think its mainly the appetizers that are the most unusual - and they aren't included on the
DDP any longer anyway.
Selections for dinner there could include:
Demi poulet fermier a la broche pommes puree au basilic et tomate braisee - Half of an all natural rotisserie chicken, basil-flavored mashed potatoes and braised tomato. (For the most part, the meal is a rotisserie chicken - unless you dislike basil or a braised tomato, this is a fairly normal meal)
Filet de boeuf grille, sauce au poivre noir Gratin Dauphinois et haricots verts - Grilled tenderloin of beef with black pepper sauce, original potato gratin of Savoy and green beans. (Beef tenderloin, a fairly normal sauce being pepper based green beans and cheesy potato - my mom made this - although not with the fancy name and presentation)
Gratin de macaroni - Baked macaroni with cream and gruyere cheese. (It's mac and cheese - the only problem being if you don't like that kind of cheese)
Jarret d'agneau aux haricots blanc - Braised lamb shank with navy beans. (Again, nothing too different here)
Lasagnes de legumes du soleil a l'huile d'olive au thym - Zucchini, eggplant, bell peppers, onions and tomato baked into thin layers of pasta. (Veggie lasagna - only a problem if you don't like those kinds of veggies)
Plat de cote de boeuf au cabernet et polenta de Savoie - Beef short ribs braised in Cabernet wine on a bed of polenta. (Also fairly normal - polenta being - I think - corn based. Only a problem if you don't like red wine)
Some of the other dishes might be a little different - but French cuisine really isn't that adventerous, even if it sounds like it is.
So, while it is true that LC has non-adventerous fare, so do these other two restaurants - however, LC still has a couple of advantages over R&C and Chefs.
R&C actually has the fewest non-adventerous dishes - only two that are extremely basic. LC and Chefs are better here.
Chefs just seems more "pretentious" than LC and R&C. Face it - you're still probably wandering around the parks in shorts and Mickey T-Shirts - perhaps it just seems more appropriate to be in the nice (but more casual) settings of LC and R&C.
So, LC has non-adventerous food in a nice, but casual setting.
Anyway, that's my take on why LC might still hold a lot of popularity.
Theoretically, even Tutto Italia's menue isn't too adventerous either - and fairly casual too - perhaps the next best alternative for non-adventerous eaters at Epcot's World Showcase.
Sorry for the long post - just thought I would consider this from a menu and dining atmosphere standpoint.