In theory, bitrot shouldn't matter during media playback, but in practice, it does.
False.
Bit-rot is totally irrelevant for media playback. Bit-rot (aka silent corruption) refers to a very, very, very unlikely event where one or more stored bits changes without the storage device signaling an error. With current HDDs, these events are less likely than UREs (unrecoverable read errors), which are already 10^-14 or 10^-15 events.
A faulty SATA controller munging data is not bit-rot. And while filesystem checksumming would be able to catch that sort of error, there are other possibilities for errors in the stream from media source to media player that would be outside the realm of filesystem checksumming. Hence, you do not actually have "end to end checksumming" in the context of obtaining and playing back media.