Was the man in the tower correct in his assertion that I am not qualified to do these holding only a PPL?
Maybe he misunderstood you and thought you intended to shut the engine down for real?
Otherwise, you are the pilot in command and free to choose your own landing technique! It is totally up to you wether you want to do steep or shallow, powered or idle approaches. At airfields with prescribed traffic patterns and/or special noise abatement procedures, you should of course respect those.