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https://jsonfeed.org/ has had some preliminary traction. Of course, the reason RSS works so well is that everyone uses the same format. So you wouldn't see so much of a "switch" as a bunch of readers accepting either format, for a very, very long time. That being said, I don't see what's "wrong" with XML in this context.
Most of the complaints I've seen with the 'wrongness' of xml are centered around its human unreadability, which doesn't matter in this context. I'm curious if there's another reason.
The entire JSON spec is only about 3 pages long. (I don't know exactly how long because ECMA's webpage is down today!) I'm pretty confident that any popular JSON parser I use will abort correctly on bad JSON. There's no expansion or entities or escaping, so the parser is a pretty boring 1-to-1 translation. Give it a 1KB JSON file, and I'm going to get back a data structure that takes roughly 1KB.
XML is incredibly complicated. My operating system's XML parser has had XXE-related security bugs in the recent past -- that's OWASP bug#4, and there's a Wikipedia article about it. There's other possible attacks, like the "billion laughs attack". I'm very nervous about running an XML parser on untrusted content.