That would have been an actual strategy, and probably would have worked, but from what I could tell they just sort of fumbled around without really committing.
As I recall, the Embrace was half-hearted, the implementation was pretty standard with no Extensions, and they never really got around to an Extinguish phase, they eventually just phased out support for XMPP clients at all.
The only way I think Google's incoherence of multiple overlapping stabs at messaging over many years makes sense is as internal maneuvering and jockeying for position among execs playing chess with the various engineering teams and end users as pawns.
ISTR that they did back off of XMPP support in Google Talk to some extent a bit before that last move. Something about not allowing incoming connection requests from non-Google accounts by default IIRC.
Of course then leadership got to it :'(