Since brass, nor stone, nor earth, nor boundless sea,The idea shown in the story is that, over generations, time filters art, leaving only works that are worth caring about. The older an artwork is, the better it is. This trope does ignore that although the "test of time" is often reliable, it's not perfect. The fact that something has survived doesn't guarantee that it's actually good. This trope relies implicitly on a scarcity value law: if there's only one complete poem of Sappho's that survives, that makes it worth more than anything mass-produced these days. It's unique and irreplaceable, a fragment of a lost era. The fact that Sappho wrote in and for a world that no longer exists also means her poems and fragments are rendered abstract, and require study to fully understand — therefore, this trope also invokes True Art Is Incomprehensible, to a degree. Furthermore, an overly strict adherence to this trope can result in a mindset that views any art that originates after a certain point to be lesser than that which precedes it. In addition, from a purely statistical basis (due to population growth, improved leisure time, et cetera), it's extremely likely that there are more contemporary works of art than have been created in the earlier days of human history; even taking into account the number of works from previous eras that no longer exist, there were still comparatively few compared to how many are produced today. Compare Nostalgia Filter, which is this trope on a smaller timescale.
But sad mortality o'ersways their power,
How with this rage shall beauty hold a plea,
Whose action is no stronger than a flower?
O how shall summer's honey breath hold out
Against the wrackful siege of batt'ring days,
When rocks impregnable are not so stout,
Nor gates of steel so strong but time decays?
O fearful meditation! Where, alack,
Shall time's best jewel from time's chest lie hid?
Or what strong hand can hold his swift foot back?
Or who his spoil or beauty can forbid?
O none, unless this miracle have might,
That in black ink my love may still shine bright.
— William Shakespeare, Sonnet 65