[Gigachad]

The only time you'd ever want to do this is for image and video formats. And HTML has built in support for this in the picture and video tags. Otherwise this sounds nonsensical.

What kind of situation would you ever have a request like "Uh I want json the most but XML could work". Either the backend serves it in a format or not, just directly request what you want.

[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.