There is no ultimate/universal/perfect way to learn or practice.
A student can need to practice a certain difficult piece with
hands separate for a while and another will learn faster/better
practicing hands together from the start. As long as the student
can play the piece right in the end, it really doesn't matter. I
don't think memory slips have anything to do with practicing
hands separate or together. For certain pieces, practicing hands
individually can help define the main lines at first, for
example when the LH and RH parts combine unconventional rhythms.
But since anyway one will need to play the piece using both
hands, I really don't focus much on separating the hands for
pieces with simpler rhythms. The problem with systematic
"separate then both hands" practice is that certain people can
feel the transition from one to the other too brutal, depending
on the piece. An alternate method (that I would qualify of "in
between") I often do myself is : I play both LH + RH parts as
written, except I force