Why do a lot of new low cost IoT modules use a MIPS 24K processor rather than ARM?
These basically inherit from the now very long history of MIPS-based, external-RAM wifi routers running Embedded Linux or various other full-featured embedded operating systems.  Effectively the resulting products are routers that no longer route, and have assorted gadgetry in place of blinkenlights on their GPIOs.

As for why those are MIPS, because people started building them that way before the large embedded ARM parts were as dominant as they have become in the past decade.  Some of the licensing deals for the cores may well now be fairly entrenched.

Note that there is little comparison to a "small" ARM part like a Cortex M3, which is designed to run from internal flash with limited storage in internal static RAM (there are Cortex M3's with external memory buses, but it's not their common strength).  There are of course IoT solutions with a Cortex M3 or M4 at their heart (WICED, etc) but typically for more constrained needs.  And they aren't necessarily that much cheaper.

The ARM parts that would be more directly comparable are the trailing-edge tablet, phone, and set-top box chips - but these are less likely to have wifi tightly integrated.