[naasking]

XML, JSON, Protobuf can all be used as object serialization formats. It's not nonsensical at all for an endpoint to offer choice as to what serialization format a client may want to use. It's not common, but that doesn't mean nonsensical.

[Gigachad]

The client can request the URL that gets the type of response it wants. There is no advantage of using the accept header.

[naasking]

URLs are much longer, harder to remember and harder to communicate than accept header values. It also unnecessarily complicates the API. It also relies on out-of-band/non-standardized information to know which URL returns which format, where the accept headers is in-band/standardize information for specifying the return format. Seems like there are more multiple advantages.