None whatsoever, as long as you don’t make a habit of it. Obviously no avios or Tier Points for the missed sector, but an overnight connection at LHR makes it far easier to short check your bag to LHR and saves you asking for it then wait, which would be the case in your proposed plan, as it will have gone somewhere else, not arrivals due to being in transit. If you plan an overnight stay (within 24hrs) then you can simply ask for it to be tagged to LHR only as you have an overnight