Might it be easier to just build a dedicated sort of line for each room? Like a part of the wall that opens up and is connected to the kitchen/wherever, to deliver your food. Would be harder at first but it'd be much easier down the line, and more efficient.
I actually worked in a hospital where they paid for robots to deliver medical records to doctors/nurses. The nurse would request records, and then the medical records department would fill it up and send them out. I think that didnt last too long, not efficient enough.
hotels rent space. your suggestion limits space. do you think that the advantage of robot server compared to humans would offset the huge decrease in available space to rent?