True, there's a wide space of breads and cheeses, but I can walk into a restaurant and order a grilled cheese and with no follow-up questions be served the restaurant's version a grilled cheese. The same could not be said of ordering a "sandwich"; the waiter would certainly demand clarification before accepting the order.
The conversation could go like this, "I'll have a grilled cheese" -- "What kind of cheese?" -- "surprise me" -- "What kind of bread?" -- "surprise me" -- "Do you want tomato or bacon or any other meats?". At this point I'd have to stop and figure out which way I wanted to go. But that's reasonable because these are non-default options; if I asked for a surprise sandwich and the waiter asked me "is open-faced okay" or "is ice cream sandwich okay" or "is a wrap okay" then I'd totally accept that as a clarification, but without that clarification none of those would be acceptable.
The conversation could go like this, "I'll have a grilled cheese" -- "What kind of cheese?" -- "surprise me" -- "What kind of bread?" -- "surprise me" -- "Do you want tomato or bacon or any other meats?". At this point I'd have to stop and figure out which way I wanted to go. But that's reasonable because these are non-default options; if I asked for a surprise sandwich and the waiter asked me "is open-faced okay" or "is ice cream sandwich okay" or "is a wrap okay" then I'd totally accept that as a clarification, but without that clarification none of those would be acceptable.