I was suprised by this whole theory myself when I came from flying at Purdue, where we liberally used the carb-heat abeam the numbers, until we turned off the runway, to when I taught in C152/C172 where I taught to use it abeam until you were on final(My teaching is this would allow max power available for a go around, and in the time it takes to get to the base-final point, everything should be gone if there was contamination anyways). Then I flew with some "ole" boys in an archer who said you don't need to use it.
Honestly, take it for what it's worth, but I'd at least clear the engine for 30 seconds sometime prior to landing. What's it really hurt? When airborn, you are above move particulate matter that the filters are meant to keep out of the engine, so providing some unfiltered air at or above pattern altitude isn't going to threaten the engine. BTW, there's not a fuel-injected archer that I know of. They are equipped with O-360 lycomings, not IO-360's as the Arrow's are.
You'll run into a lot of "old" teachings out there that aren't necessarily true. Like running a constant speed prop engine "over-square." It's actually better to run them that way, but I digress.