There are a few factors that are considered- more secular, more fun, more interesting songs, costuming demands, parts, teachers fancy a change, parent competition (a cohort of very pushy parents can cause carnage with a traditional nativity).
One big sway our school had was the fact most of them have extra parts. The traditional nativity story has limited parts (unless you are including a huge flock of sheep, horses for the wise men, lots of inn keepers, choirs of angels). The more quirky ones tend to have more parts and more diversity of roles and speaking parts - some have a better spread of parts and less "main" parts with more speaking parts (essential if you have a very pushy parent cohort). Many schools are 2 form if not larger and usually it is 1 xmas show per year group so you are looking at 50-60 kids all needing parts.
Nativity rehearsals go on for ages and it can get very dull for everyone. The quirky ones do tend to have a bit more action for more participants in them and better songs (often with actions for everyone to do). Costuming is also important to consider, alongside the parent participation levels (and competition) at the school. Some quirkier ones don't need a lot of costumes making or are simple to put together with everyday clothes. Costuming can be a headache, you always get the sewing bee competitors, the amazon buyers, the ones who forget, the working mums cobbling things together best they can on limited time, the hand me down/ across costumes that have been through 6 kids and 3 different schools and my personal favourite - Ive made my child a made to measure Mary/ Joseph costume so they can play Mary/ Joseph (child is actually a sheep in the play). Someone is always upset.
Although biggest reason for less traditional nativity ime is parts, enjoyment for the children and fancying a change.