The recommendation to use a water dampened applicator to apply waxes has been around as long as car waxes have been around from all the years I've been reading and studying this topic specifically and detailing in general.
My guess as to why companies recommend this are,
- Dampening, or wetting an applicator pad tends to make it softer
- A dampened applicator will absorb less product because it's already wet with water
Those are the two I can think of, there might be more.
Dampening the applicator pad to make it softer and so that it won't absorb your precious wax are great ideas but another approach is to dampen your applicator pad with the product you're using and avoid water. I show that with the Wolfgang Paint Sealant in the below video and share how to get a paste wax out of a container in the Pinnacle Video.
Wax and water don't mix, paint sealant and water don't usually mix and for what it's worth, I'm a big fan of not adding water to your waxes and paint sealants when using them as your LSP or last step product.
We didn't have microfiber till sometime in the 1990's for car detailing, so the recommendation to wet your cotton, terry cloth applicators to make them softer is because cotton is normally less soft than microfiber so dampening it will make if softer.
There are some very soft cottons on the market thus I couch my words in the above paragraph.
Normally, foam and/or microfiber applicator pads are considered to be more gentle to a scratch-sensitive finish like a modern clear coat finish, but you should still always be sure that your applicator pads are clean before and during use as anytime during the application process it's entirely possible to pick up a stray dirt particle and you don't want to rub this all over the paint.
In one of the below videos I cover "inspecting" your applicator pad as a "Best Practice" while waxing your car.
My personal preference is to apply all waxes and paint sealants using a Porter Cable 7424XP polisher because your hand cannot duplicate the even and consistent pressure and coverage provided by a soft foam pad on a DA Polisher.
I don't buy off on the bare hand application touted by others but do recommend everyone try it at least once so they have their "own" opinion and a valid one at that.
I can probably find my comments on bare hand application of wax on MOL as I addressed this a long time ago when it became the new, old hot topic again...
