this claim is not really relevant for the doomsday argument, you only need the random sampling of the index of someone, you use you, because you are random choice. it doesn’t matter that you can’t be another you.
this claim can be interesting regarding SIA, but even there i don’t think it holds, but it will be more interesting and nuance.
I am nor sure that me willing to accept to be paid X to stay in the hostel, is similar to me willing to pay X/n for someone else to say there.
Say it is only me and another person, hotel cost 100$, hostel cost 50$, i am willing to stay in the hostel for 100$.
If i am staying in the hostel, i will get 100$ and pay 50$, meaning i will have +50$ - which i am happy with since i ask for the 100$
If i am staying in the hotel, i might pay the other person up to 100$, meaning i will spent up to 200$ - which i may be very annoy by, since now the hotel may not be worth the cost.
There a very realistic scenario here, in which there no balance between people cost of accepting to stay in the hostel, and the cost they willing to spend on the vacation/hotel.