The use of slatted racks doesn't - as far as I know - have anything to do with honey yield.
Miller's original idea was that the rack was removable, to be inserted - as required - into a void beneath the bottom box. This feature appears to have been lost over time. As can be seen from Miller's photo, unlike modern woodenware it was a very crude affair:
Miller's idea was taken-up by Killion who used them all-year round, and so built them as a fixed hive feature, rather than being removable. He spoke highly of them, writing that they help to prevent swarming and aid with the evaporation of nectar, as well as providing much needed ventilation.
As can be seen in both of the above photographs, the slats ran crosswise - that is, at ninety degrees to the orientation of the combs. For some strange reason, people seem to have got it into their heads that the slats must run lengthways, and that each gap needs to coincide with the comb directly above it. I've even seen plans which incorporate tubes, and even wedge-shaped slats (apex pointing upwards) with claims that these facilitate the directing of falling debris towards the mesh below. Total overkill, and completely unnecessary.
Personally, I think they're great, and have never seen a single example of bearding in a hive with one fitted. Many people think bearding is perfectly normal - I don't - I think it's an indicator of poor hive design. Imo, bees should be able to get off the combs when congested during hot weather without leaving the security of the beehive, and the slatted rack enables them to do this.
PS - as MB has already mentioned, it's the space beneath the slats which is the really important feature - all the slats do is to prevent comb from being built in that space.