Subject is defined as the argument which agrees with the affixes of the verb. But if a language does not have inflectional affixes, can you state that this particular language does not have syntactic functions ?
"Subject" is not defined as the argument which agrees with the affixes of the verb. Sometimes, "subject" is defined as that argument which verbs agree with. In the modern era, you might start with the paper by Ed Keenan, "Towards a universal definition of “subject”", in Li (ed) 1975 Subject and topic. Keenan had about 30 properties that he associated with subjecthood, which are not all necessary or sufficient. There is a methodological problem with the concept of "definition" in linguistics, that we don't have a theory of what a "definition" is, so one might present "a fundamental characteristic of a thing" as part of the definition of the thing. Or, one might present identificational diagnostics as part of the "definition" of a thing.