They literally have no power beyond acting as a gatekeeper for their users. Their omnisearch (which was awful, at least the last time I used it) is a major part of their strategy to try and guide users towards content they profit from.
Given that it's Google's job to guard the UX of their Roku apps, I think it's 100% reasonable for them to tell Roku to add HW support for new features and not gimp search inside the YT app.
I could see this argument if a search for music would lead to a search for (say) a music video. But the idea, as I understand it, is that a request for music to be played would instead be routed through YouTube Music. Even if I'm in the YouTube app, I'm not going to want my music search to go through YouTube Music -- I'm not a subscriber.
LGs TVs have a prominent omni search button. If you’re in the YT app and use the omnisearch it searches across all content services you have connected. It’s an amazingly useful feature and makes the TV experience actually feel integrated. First time I’ve been happy with a “smart” TV experience.
I’d say it’s a fair comparison.