Why is this that-clause a subordinate?

she was so tired that she couldn’t think. (Oxford)

Oxford says that-clause above is a subordinate clause expressing a result. Semantically ‘she was tired’ seems to be the main clause, but there also is the possibility ‘she couldn’t think’ might be thought as the main one, and ‘she was tired’ is a subordinate expressing the reason of that-clause.

So the words below that do not use ‘subordinate’ sound to be better explanations for the case. Then on what ground does Oxford say the clause is subordinate?

Cambridge: to introduce a clause that gives further information, although it can often be left out. Longman: to introduce a clause that shows the result of something:

The fact (if it is a fact) that it has the most important information is irrelevant; subordinate refers to the clause's syntactic role.

Syntactically, that she couldn't think is only the back half of the so ... that construction, which itself is syntactically the back half - the complement - of the predicate (or Verb Phrase, if you prefer) of the main clause.

Syntactical terminology is about how the pieces fit together, not what they mean. Syntactically the keystone of the entire sentence is was, which doesn't actually mean anything: it's just a hook to hang the tense on.