There is no dive and drive or level off at MDA in our operation (dive and drive is considered an unsafe operation and will prevent passing an IOSA audit). All non precision approaches are done on a relative glidepath that respects all minimum altitudes with a mandatory go-around 50 ft above MDA if no visual contact. So the usual VS during a non precision approach (standard is to fly it fully configured) is somewhere between 550fpm and 800fpm, not 1200 which would of course violate our SOPs.
And yes, of course if you do nothing the autopilot will happily descent you into the ground operated like this, that is why we have mandatory approaching minimum, minimum and 500' callouts as gates where decisions can and should be made.
To switch back at 500' above MDA is actually something that originally stems from a boeing recommendation for VNAV flown approaches and the current drive with boeing is to have the same procedure for every kind of approach, which is why all our new delivered planes since 2006 have IAN capability which assures ILS like procedures and safety nets for every kind of approach, not VNAV/LNAV or VS for non precision approaches anymore.