The ancient quarrel between poetry and philosophy
Philosophers from Plato to Heidegger have seen a fundamental tension or incompatibility between philosophy and poetry. The 'ancient quarrel' quote is from Plato, Republic 10.607b 5 and c 3. Plato's own quarrel with poetry appears rather local :
Gould understands Plato's "ancient quarrel between philosophy and poetry" (Rep.
10, 607b5-6) to be, au fond, a conflict between two world-views, and, equally, between their psychological roots: on the one side, "philosophy," which means a
craving for, and faith in, an ultimate order of justice; on the other, "poetry," which means the human yearning to believe in the injustice of existence. (Stephen Halliwell, ' The Ancient Quarrel between Poetry and Philosophy by Thomas Gould', Classical Philology, Vol. 87, No. 3 (Jul., 1992), pp. 263-269 : 264.)
There is clearly no reason, beyond the cultural contingencies of ancient Greece, why poetry as such should be wedded to a view of the injustice of human existence.
Heidegger adopts :
position in Was ist das—die Philosophie? (What is philosophy?): ‘‘Between
these two — thought [= philosophy] and poetry — reigns a hidden relationship because
both are given to the service of language and give themselves to it. Between
them, however, there persists at the same time a deep abyss, for ‘they live
on separate mountains.’’’. (Brenda Deen Schildgen, 'Animals, Poetry, Philosophy, and Dante's Commedia', Modern Philology, Vol. 108, No. 1 (August 2010), pp. 20-44 : 22.)
Philosophy is (in basic terms) a mode of inquiry. Poetry is (in basic terms) a mode of expression. I can't see any reason a priori why philosophy cannot be expressed through poetry.
Poetry can be philosophical in two ways.
▻ Poetry can be, and this is true of Dante's La Divina Comedia ('Divine Comedy'), informed by philosophical preconceptions. Ideas from St Thomas Aquinas, Aristotle (maestro di color che sanno - 'master of those who know', in Dante's words) and to a less extent Plato are the essential framework of the work.
▻ Poetry can also express and expound philosophical views : Lucretius' 'De rerum natura' ('On the Nature of Things') is poetry - a poem that sets out the main ideas and arguments of Epicurean philosophy on what the world is made of, what is the road to happiness, what happens after death, and other philosophical topics. Here is Greek philosophy set out in Latin verse.
Philosophical and poetic quotes
The satirical poetic comedies of Aristophanes describe philosophy in single lines : you can find this in Nephelai ('The Clouds'), which sends up (not very accurately but that is contingent) the philosophy of Socrates. Equally your quote from David Schmidtz, Life is a house and meaning is what makes it home, might be counted as expressing a kind of broadly philosophical view in the imaginative, compressed metaphor that one often finds in poetry.