if you look at the dilution rates of some thing like F90 at 500-1 you recover 80% of the solution you put down, so on an average carpet you will leave less than half a teaspoon of chemical spread across the full carpet, most of which will powder up upon drying and be vacced out.
why is their a problem with rinsing with a detergents? resoling, sticky residue, chemical sensitivity, are all carpet cleaning urban myths passed on from one inexperienced carpet cleaner to another.
you can usually tell the experienced as they tend it use washing machines & hair washing as valid arguments against detergent rinsing
which is a bit like me say "you wouldn't play football with a pork pie"... a totally irrelevant point