Should you request graduate school recommendation letters only from those that know you as a researcher?
Graduate schools admitting students are looking for evidence of ability as (or at least strong potential to become) a good researcher. Therefore, letters of recommendation that do not discuss research at all are simply not nearly as helpful to us than letters that do.

However, a mediocre letter of recommendation can be damaging to a student's chances of admission. Someone who isn't enthusiastic and immediately willing to write a letter should not be asked to write one; the "hit" to the student's admission chances simply aren't worth it.

So, under the circumstances, someone who is willing to write a very good letter that can testify to academic talent is certainly better than a weak to mediocre research-based letter. But a letter that only talks about a student taking tests well and "acing" a class is not really helpful. A letter that talks about, for instance, an in-depth class assignment, or can include details and observations from outside of class, would make for a much stronger and more useful letter.