When I first learnt and later taught solid state physics the concept of a quasi-particle only came up in the context of Fermi liquid theory.
Yet, quasi-particles are a profound and central concept of quantum many-body theory. Hence, it is important that students be exposed to this idea as soon and as much as possible.
I probably slowly started to appreciate this by looking at Phil Anderson's classic Concepts in Solids. It is based on lectures given at Cambridge in 1961-2, and inspired Josephson to invent his effect.
The second half of the book is all about quasi-particles.
So when teaching "Ashcroft and Mermin" there are several distinct opportunities to introduce quasi-particles, besides in the context of Fermi liquid theory.
These are holes, phonons, and magnons in a ferromagnet.
The case of holes I discussed earlier.
I was both embarrassed and pleased that when I taught magnons this year, one of the students asked, "Aren't these quasi-particles?"
For phonons I have a confession. In the solid state course we currently "skip" the whole subject. We just can't find the space/time. I feel things like Fermi liquid theory, semiconductors, magnetism, and superconductivity are more important. The students learn a little about phonons in an earlier statistical mechanics course.
There is some irony in me skipping the topic. When I first came to UQ for a job interview I had to give a lecture to a live undergrad class. The assigned topic was phonons in the solid state course.