Is it normal for a hammer drill bit to wobble?
I have 3 or 4 hammer drills some combo units and 1 is just a large hammer / demo drill model. None of mine have the wobble you are describing brands I have are hilti, dewalt and milwaukee. For tile I would not use a hammer function but a standard drill and a diamond coated or carbide / grit coated bit. I would think the hammer action will crack the tile, I am sure it would on most natural stone tiles as they tend to crack with a wet diamond saw.