Doomsday argument and simulation argument are quite bizarre for most people. But these are not the only strange theories one can come up with when employing anthropics.
It is likely to have an unusual high IQ.
Perhaps brain works in a way, that having high IQ correlates with something that also causes more observer moments. Hence there are more of high IQ experience in the world than that of low IQ.
Total universe destroying physical catastrophes that expands in speed of light (say false vacuum collapse) could be very frequent. As much, as once every second. And it is only due to survivor bias that we think universe is stable and safe. How would we know?
Animals does not have consciousness
There are more animals than humans on Earth. Still we find ourselves as humans. Perhaps it is because we only can be humans, as only humans have consciousness.
We are stuck inside infinite loop
Lets assume simulation argument is correct. Then we probably exist inside simulation, run by some software. All software have bugs. One of the bugs software sometimes have is getting itself in an infinite loop. Biggest amount of experience computed by this software then could possibly be inside this infinite loop.