The doomsday assumption makes the assumptions that:

We are randomly selected from all the observers who will ever exist.

Actually, it requires that we be selected from a small subset of these observers, such as "humans" or "conscious entities" or, perhaps most appropriate, "beings capable of reflecting on this problem".

They are wiped out by a catastrophic event, rather than slowly dwindling

Well, for the numbers to work out, there would have to be a sharp drop-off before the slow-dwindling, which is roughly as worrisome as a "pure doomsday".