As a retailer of dive masks, we frequently deal this issue. Dive masks should not persistently fog if the glass is reasonably clean. A more illuminating question is "WHY does my recently purchased dive mask persistently fog unless repeatedly treated with some kind of defog ritual?"
The answer for the primary cause of persistent fogging was supplied to us by the late Noel Brown, who established Oceanways & SeaDive brands - one of the most long established and well known manufacturer and distributor of dive masks. The cause is the mold release chemical used in the manufacture of the flexible silicone skirt. The mold release agents are volatile by their nature and during storage will migrate to the surface of the lens to cause fogging. This is often the case when the mask has been sealed in an air-tight box or plastic bag. These stubborn deposits can be safely removed with an extra application of a powerful non-abrasive
surfactant like liquid dish soap, baby shampoo, or the commercial mask cleaners.
The mask may persistently fog at first, requiring repeated cleaning, but with the passage of time the mold release agents will dissipate naturally and the issue will resolve itself. To hasten the dissipation of the mold release agents from the mask silicone, store the mask so that it is exposed to air between dive trips and
avoid the use of sealed boxes or use a sealed box only for transport in the dive bag. (This is why our own DGX Gears brand masks ship with a padded mesh bag rather than a plastic box.) Do NOT let the mask get hot during transport, i.e. keep your dive bag (or at least the mask box) out of the sun.
Don't use toothpaste or any other other abrasive on modern dive masks, especially those masks that have optical quality ultra-clear glass lenses, vision correction lenses or 'optical coatings' on the lenses. You will either damage the lenses, or needlessly waste toothpaste since most modern toothpaste formulations are not at all abrasive nor are they particularly effective as a surfactant.
A secondary cause of persistent fogging is that most open-circuit divers have the unconscious habit of dribbling warm moist gas out their nose during the exhale, which then dribbles out the edges of their mask skirt and is camouflaged by their second stage exhaust. This is very noticeable when training new closed-circuit rebreather divers where the tiny bubbles are now easily observed. It can take as much as an hour to teach CCR students to stop dribbling gas out their nose when they exhale out their mouth and some never stop completely... the moment they become task loaded the behavior returns. Instead of using a surfactant cleaner, the divers that have issues with persistent fogging on even well cured masks as a result of leaking gas out their nose during exhale will benefit from using one of the defog gel coatings that inhibit the fog formation.