Explanation
Burned-in text is not primarily an accessibility feature in this context, though it is that too. It is the delivery mechanism: a video whose meaning lives only in the audio has failed for the majority of the people it reaches, before any question of quality arises.
Timing, weight and line breaks are the whole visual craft here, particularly for formats with nothing else on screen. Treating subtitles as a subtitle track rather than as design is why most podcast clips look identical and few of them perform.
The common mistake
Letting the subtitles lead the audio. Text that lags speech slightly reads as natural, and text that arrives before the word is spoken feels broken in a way viewers notice without being able to name.