It seems a lot of courses (like this and this) on theory/models of computation (and even formal languages) cover DFA, NDFA, PDA, and TM in the order of increasing computational power. This of course makes sense, but why aren't various other computation models included in general? For example, we could take the route from untyped lambda calculus to simply typed lambda calculus and so on with decreasing expressiveness. (I know they are detailed in PLT, but aren't they models of computation as well?)
In brief, since all the above (and a lot more) count as different models of computation with different powers, is there any specific reason, historical or else, that the machine-like models are adopted, sometimes even exclusively?