Halliday & Matthiessen (2014: 141):
… the term ‘Subject’ as we are using it corresponds to the ‘grammatical Subject’ of earlier terminology; but it is being reinterpreted here in functional terms. The Subject is not a purely formal category; like other grammatical functions it is semantic in origin.
Halliday & Matthiessen (2014: 149-50):
The notion of the Subject as a ‘purely syntactic’ element arose because it proved difficult to understand Subject + Predicate in an account of the grammar that recognised only the ideational kind of meaning; once we open up the other metafunctional spaces, just as Theme comes powerfully into the picture, so Subject becomes (equally powerful but) less mysterious.
The notion of Subject as a syntactic category is maintained in the Cardiff Grammar. See here for some of Fawcett's misunderstandings of Systemic Functional Theory in the Cardiff Grammar.