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 a ppp
on one hand or the other. Just like if you would turn a volume/balance knob between the hands. For example, using this method I can "check" if a particular LH passage (in a piece I don't master yet) sounds legato enough, if its accents are done just right, etc. Otherwise, if I play the same passage with the RH at written volume, I wouldn't hear possible mistakes in the LH. This method forces you to play both parts, even though one hand is played so soft it's barely heard. IMHO, this forces one to be more involved and put more attention in the playing. Of course, this can't be applied to all students or pieces, but very often it helps me perfect the playing and the memory.
Note that I would not force or recommend this method on a student. But with me it works.