That’s the difference between all the integers (from negative infinity to positive infinity) vs just the natural numbers (from 0 to positive infinity). You can have infinitely many guests starting from a particular first guest.
In that case I'd probably rephrase my original objection to say the "next guest" has nowhere to go, except when the they depend on the "next next" (etc.) guest finding a room in a "full" hotel - but I can see how that situation "never" comes up since they can pass the burden along infinitely.
I just feel like someday at the end of time, this poor unassuming new guest is gonna get cheated out of a room..