Currently reading Plutarch, and this is one of the footnotes: "Simonides was one of the most famous Greek poets. His work survives only in fragments"
Why does Homer's work survive but Simonides' doesn't? The same applies to writers like Plutarch, who made references to many well respected historians whose work also doesn't survive.
The selection of which authors survive and which ones don't isn't a choice that anyone made, it's a result of many phases of selection. If a literary poet got into the school curriculum or was a subject of scholastic interest in 10th century Byzantine schools, then they survived. If not, their chances were reduced. Not a single early lyric poet made the cut: the sole exception is Pindar, and even then only in two manuscripts. (Bacchylides too, but only by a complete fluke of a relatively intact papyrus being found.)
Homer, by contrast, survives in hundreds of manuscripts. But not all of Homer. Most poetry attributed to Homer in antiquity (like the Thebaid), and literally everything by every other epic poet of that period, does not survive. (Unless you count the two surviving Hesiodic poems as 'epic'.)
Poets' popularity in their own time only determined whether they had a starting chance at surviving. But every subsequent generation made its pick too. In every period, poets survived if people wanted to read them, and when people didn't, their chances dwindled. And, given enough time, that weeded out nearly every poet.
It so happens that the Iliad and Odyssey are just about the only poems from that time that never lost their popularity in the Greek world, once they hit the big time in the late 500s BCE. Those two poems got off to a really strong start in the 520s, with performances mandated in a major Athenian civic festival, being a central element of elite education, masses of scholarship written about them in the Hellenistic and early Roman eras, and unparalleled influence on the visual arts. All these things together gave them enough momentum to survive until the Byzantine renaissance of the 9th-10th centuries CE. It's only from that point on that any poem's survival can be said to be more or less assured.
I've written some responses on related subjects before that may help fill in some gaps:
In addition to the great KiwiHellenist answer, there is something more that could be useful to note: to put it in terms of authors is a bit misleading. To stick with your exempla, Simonides was a (very influential) poet on which we have many biographical informations and details. Instead, we do not and probably will never know if Homer really existed or not: his existence is so much debated to be eloquently formalized in what is renowned as 'The Homeric Question', to which generations of scholars devoted their life. Someone says he really existed, someone not, someone that he is the unification of two different people, etc. What is almost certain is that Iliad and Hodyssey derive from oral tradition, attributed at some point to Homer. Also, that they gained tremendous relevance already in ancient Greece. Also, that Homer as a mythical figure gained similar relevance. Nevertheless, we also know that there were six other poems composing what is now called the Epic Cycle, regarding Troy war: they were in the past variously all attributed to Homer or other poets, while more recently to other poets. The existence of these poets is also semi-legendary in most cases, and these poems were all lost during the centuries. So