In my previous company weeks were the timescale of choice and the main issue was about prior year comparative where it would go out of sync so would need to create a mapping module and "fix" the ones where the logic didn't work.
There is one model currently that we use where fake-time is being used but this is mostly because of needing to roll-up to real months and we haven't had the bandwidth to actually fix it so that we can use model time and all the benefits that brings (it's an internal team model so doesn't impact anyone)
We have a 53 week year around every 7 years and the Anaplan calendar doesn't align with ours. I've looked at using it before but it didn't seem to work for us as it wasn't flexible enough in terms of selecting which year the 53 week year applies to and which week is the 53rd week.
As a result we use fake week time lists where we need to. Challenges are around maintaining and using these alongside Anaplan time for days and months. Obviously all do-able in terms of workarounds but just a bit of a pain and added complication.