Actually, where I studied, Unit-testing (let alone TDD) wasn't mentioned until a very late stage during my studies.
This is very unfortunate, and one of the reasons some devs are having a hard time to start writing tests.
These points you've made should be explained during the first CS intro course, this way it'll be easier for us to convince (if necessary) new devs to write unit tests and maybe even employ TDD.
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Actually, where I studied, Unit-testing (let alone TDD) wasn't mentioned until a very late stage during my studies.
This is very unfortunate, and one of the reasons some devs are having a hard time to start writing tests.
These points you've made should be explained during the first CS intro course, this way it'll be easier for us to convince (if necessary) new devs to write unit tests and maybe even employ TDD.