Maybe chat just doesn't make them any money so they don't really give a shit and all of these things are pet projects that get shut down on a whim?

The key to Google is that their real Users are advertisers. That's it. The "users" you're talking about are the product they're selling to their real Users(Advertisers).

Reality is that all these products are result of autonomy given to teams - it's not really pushed top-down, so new 'innovative' ideas are spearheaded and pushed up for strategy's adoption.

PS. Please don't call that chrome window a desktop app.