It's a very impoverished form of composition if the only things you can really compose are the absolute primitives, rather than allowing you to compose things t

It's a very impoverished form of composition if the only things you can really compose are the absolute primitives, rather than allowing you to compose things that are themselves composed. When you "program" with Turing machines, you don't have a way to take a section of "code" and paste it into another, larger program. You'll have to deal with two pieces numbering their states the same, overwriting each other's tape data, etc. If you have two Turing machines that solve separate pieces of the problem, you know there exists a single machine that does both things, but nobody actually goes and constructs that machine. Instead, they just mention its existence as justification for writing "do this; do that;" in a higher-level machine description.