I would hesitate to rely on GPS height for the flare and touchdown
AFAIK all autoland systems use a radar altimeter for the flare portion. I guess the autopilot switches over to the radalt at about 150ft.
WAAS (EGNOS in Europe) facilitates GPS approaches with a synthetic glideslope but the DH on these is still about 200ft (no European ones are published since none exist) i.e. no better than Cat 1 ILS.