Most of us, and certainly the major texts, would consider a valid variety to be a reflection of the design (including possible errors) punched/engraved on the die, rather than subsequent die wear or impairment due to accumulated crud. However there are a few notable exceptions such as the ONF penny which seem to have developed a following. Otherwise striking errors are considered more of an interesting curiosity than true variety, though they do have specialist collectors.
Clearly, but rarely, things can change. In the case of your penny, if it could be positively demonstrated that the Royal Mint (or Heaton) did produce a small run of intentionally 'no H' pennies, then an altogether different view might be taken.
It certainly is unusual for the H to be totally absent, so enjoy the coin for itself and the debate it can generate.
Jerry