Should I take PhD application recommendation letter from academic advisor?
Speaking from social sciences:

If it's easy for both parties to produce the letter, go ahead and have it. It wouldn't hurt, and perhaps you can suggest some general stuff that is absent from more specialized letters.

If it's too much hassle, then simply have an agreement to have the letter produced "later on" if it's wanted.

Your view about such letters is generally on the money: they refer to either class or research performance. But perhaps there are aspects that your advisor's letter can highlight. Bear in mind that many applications, etc., ask for a maximum of letters - so, if you already filled it with specialized letters, then this general one won't be needed.