I used to always take Traveller's Checks exclusively. I never had a problem using them anywhere, but yes, they can ask for a phot ID at any time. That was never a problem becaues I always carry my driver's license with me in case there is a problem with my AP or I get carded when buying alcohol. But I disagree that they are the most efficient method of payment. Charging back to your room is the most efficient, and charging to a credit card is right there too. I love being able to charge back to my room and not having to worry about if I brought too much in traveler's checks with me or what to do with cash when I get change. I actually did lose a traveller's check last fall when I went. I'm assuming it was when I was pulling something out of my bag and I had a lose check in there and it fell out. American Express was excellent about replacing it. It was at my house by the time I returned from vacation. So it is definitely much safter than cash. But with the credit card/room charge, I don't even have to worry about the TC's and keeping track of which serial numbers I've spent.
As far as how much per food per day, it really depends on how much counter service vs sit down restaurants you do. I've found that when I used mainly counter service with maybe 2 sit down meals (in a week), I average about 35 a day, including snacks and bottles of water. I wouldn't consider myself a 'big' eater, but I do like to snack and I drink a LOT of bottled water.