Dual slope converter vs. delta-sigma converter?
With a dual-slope ADC you effectively get free averaging as the run-up integration phase will have this effect.  The output is also extremely simple, just a pulse that needs to be timed which can be done with even the simplest micro controllers.  

$4 is a really big deal when your making 50,000 of something and trying to sell it for $50.  The dual-slope part you linked is $1.64 in a PDIP for 5000+.  The sigma-delta's cheapest package is $2.88 in its cheapest package.  Saving ~$1.20 on a single part AND being able to use a more basic microcontroller is a big cost win.

I think you'll find the more expensive multimeters do use higher end ADCs.