Why doesn't the auxiliary will qualify as future tense?

Solution 1:

The author seems inconsistent to me.

I am someone who says that English doesn't have a future tense, but that is because I limit what is counted as 'tense' to what is morphologically marked (i.e., by verb inflection.)

But if you're going to include auxiliaries in the tense system, then will would surely qualify.

I can think of only one way for what you've quoted to not be inconsistent: if they meant that a language can mark tense either by verb inflection or auxiliaries, but not both. If that is what they meant, then because English clearly does mark the past tense morphologically, will would be excluded. But if that is what they meant they could have explained it rather more clearly!