I've been thinking a lot about this sort of problem recently, after reading Gibbs' Elementary Principles in Statistical Mechanics. I'd recommend you read it, as Gibbs talks about many subtle points regarding the different ensembles, and no other text that I've seen goes into so much detail.
From what I can tell, the canonical ensemble is a fundamental ensemble in its own right. While it is often "derived" in textbooks by using a microcanonical ensemble of a system combined with heat bath, it is not really necessary to assume the microcanonical ensemble. What I mean is, you can use a variety of ways to define the heat bath's ensemble, as there are many ways to get a sharply peaked function. As long as the total ensemble has reasonable macroscopic thermodynamic qualities, the canonical ensemble will pop out in the end (or grand canonical, if you allow for particles to leave) for any small part of the total system.
The origin of the universality is essentially that the heat bath's density of states tends to grow as energy^(huge power) and the typical heat bath energy of concern is a large number. Therefore the logarithm of the heat bath's density of states can be taylor expanded as a linear function, over a wide range of energies. In the thermodynamic limit (imagine taking your heat bath, replicating it 10000000x, and then merging the replicas into one giant heat bath with only the total energy conserved), the log(density of states) becomes arbitrarily linear in energy, and the probability distribution of energies for the heat bath converges to a relatively narrow gaussian (this occurs regardless of the original heat bath ensemble, by central limit theorem). Once you attach the system of concern to this giant heat bath, you invariably get the canonical ensemble for that system.
(I have been a bit vague and non-rigorous here, but I hope you get the gist.)
TLDR version: It is the linearity in log(heat bath density of states) that leads to the canonical ensemble for a system attached to the heat bath; the choice of ensemble for the heat bath is not essential.