Most athletes I'm aware of allow their heels to touch the ground. Unless you are aware of a bunch of athletes that walk around like velociraptors, and if you are, please share!
weightlifting yes, but not most track and field. It's pretty common for dancers to say "you should be able to slip a sheet of paper under the heel" for example. Pretty sure that's the case in tennis too.
As a former competitive tennis player, moving the weight to the balls of the foot is recommended when in a ready stance, or when actively shuffling. It isn't something that would be expected when walking.
