Do Ancient Greek verbs in the Simple Present tense ever imply grammatical modality?

Herbert Weir Smyth, A Greek Grammar for Colleges : §1876 on

οὗτος μὲν γὰρ ὕδωρ, ἐγὼ δ᾽ οἶνον πίνω for this man drinks water, whereas I drink wine. (habitual)

ἄγει δὲ πρὸς φῶς τὴν ἀλήθειαν χρόνος “time brings the truth to light” (gnomic)

“προδίδοτον τὴν Ἑλλάδα” they are trying to betray Greece (conative = attempt: “The idea of attempt or intention is an inference from the context and lies in the present only so far as the present does not denote completion”)

ἀπόλλυμαι “I am on the verge of ruin” (anticipation)

“εἰ αὕτη ἡ πόλις ληφθήσεται, ἔχεται καὶ ἡ πᾶσα Σικελία” if this city is taken, the whole of Sicily as well is in their power (anticipation)

χρόνῳ ἀγρεῖ Πριάμου πόλιν ἅδε κέλευθος in time this expedition will capture Priam’s city (prophecy)

I won’t count the historical/annalistic present, that isn’t modal.