Fundamentally different approaches have been taken [in the past century of research on tense and aspect … so that definitions have been based on (a) formal, (b) cognitive (c) functional or (d) real world categories. A variety of different analyses therefore becomes possible, each with its own justification. Some might want to label as future tense any verb that represents future time, so that the verb in I leave for Montreal on Saturday would then be considered future tense. For similar reasons I have read that book is considered by some to be a paste tense, e.g., Huddleston 1995:102ff, in spite of the fact that the only tense marked in the form is the present or non-past tense of the auxiliary. Here we have a confusion between what is presented (the event taking place in time) and the means of representation (the linguistic category). It is also a confusion between systemic entity and function: if I take a kitchen knife to tighten a screw, must I consequently call it a screwdriver, and refuse to call it a kitchen knife? To rely on function alone, and ignore the morphological and systemic evidence, inevitably leads to a certain amount of error and confusion.—John Hewson (1997) Tense and aspect: description and theory, in Tense and aspect in Indo-European languages: theory, typology, diachrony, John Hewson and Vit Bubenik (Amsterdam: John Benjamins), 1-2.
If we take these words seriously, we should certainly not reject the category of tense as temporal reference in the Ancient Greek verb.