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Well, I think you don't really need to go on with the “anything else”. They need a way to make their scenario work, and this answer provides exactly that. I upvoted because it is a simple and easy way to resolve — however … What if a guest decided to walk away with the phone? They could always charge them for the replacement, yes, but the overhead of time required to restock on them and to get a new replacement in the room during room service seems like a bit much.
I like this answer, though there are a few differences between the topical question and the Pony Express. For one, though they did pride themselves on speedy delivery of messages and parcels, the riders were rarely in danger of capture and whatever else like in the situation of the question. On average, though, I think it shows a certain optimum which the horses and rider in that situation would be hopeful to achieve.
To further add to what @cybernard said — a point which I missed, but then this wasn't tagged magic, so that's probably why: If you do expect to make use of any healing abilities for this, you need to explain how exactly the healing drains “energy” and how exactly it “heals”.