I don't know if its a thing in Class D amps, but as an experienced engineer I consider it a best practice that I like to do with any new electronics where possible.
I should refine my use of the term "burn in." I'm not saying that components produce audibly different output as time passes.
It's more of a colloquial industry term for running a DUT through some sort of test to ensure it's robustness.
At hp and UE, we often procured numerous sample devices from different moments in production and put them into such tests.
The objective of the testing was to give us confidence in both the design and manufacturing. More thorough reliability testing would be performed separately from what we were doing. But this early testing gave us directional indication.