Why using poetry to convey a theological or philosophical content?

There seem to be three ways a thinker could use (also) poetry:

1. 1. just as a formal device (e.g., for mnemotechnical purposes): Dharmakīrti, Kumārila, Bhartṛhari…
2. 2. as a way to convey in a dramatic way a philosophical content: Jayanta's Āgamaḍambara, Utpaladeva's stotras… In this case, the full-fledged form of one's reasoning will still be found in one's philosophical works.
3. 3. insofar as poetry and narrative allow one to integrate time within one discourse, to go beyond the logic of the principle of non contradiction, etc., : Vedānta Deśika, many Yogācāra and Mahāyāna Sūtras. In this case, one's narrative texts will be closer to one's ultimate purpose.

Do readers see further cases?

On Philosophy and Poetry and o Vedānta Deśika, see (among many other posts), here (please note also Vidya's comment). On Jayanta, see here. On Utpaladeva, see here. On a Mahāyāna Sūtra and its philosophical significance, see here.