Doing the white tile method requires the laser to run low and slow because you are more or less cladding the titanium dioxide in the paint to or even into the tile. Any time you are trying to clad anything with a laser it takes a slower speed. If you just up the power and up the speed the laser does not have enough time over substrate to get the titanium to bond or burn into the tile. What happens is you just burn the paint off of the tile. this can be seen when you remove the paint with lacquer thinner and most of the black comes off.
An interesting example of this is this. I spent about 4years as an laser engineering tech in aerospace engine repairs. Even using a 3Killowat C02 laser, with all that power, ended up about 900 watts @ 18-21 inches a MINUTE was max speed we could run, regardless of how high we cranked it.,…in order to get enough depth of penetration to allow the sintered Inconel powder to clad to the parts surface.
Yah maybe unglazed tile can run faster…the glazing definitely affects time to bond verses raw tiile