As indicated in a comment by Hari5000, zombie spawns are much rarer in deserts.
It's not completely clear how exactly the spawning of zombies and husks works in deserts, but here are two quotes from the Minecraft wiki:
In deserts, all zombies exposed to the sky have an 80% chance to be replaced by husks
Husks spawn at a light level of 7 or less in the desert, desert hills, and desert lakes biomes, mostly replacing zombies in these biomes.
This sounds to me like what actually happens is that zombie spawns are 80% reduced in deserts and husk spawns are a separate spawn mechanic that has sky access as a condition. So if you build a regular dark room spawn farm in the desert, you will get only 20% of the expected zombie spawns.