Yeah, I think it's time to get a Chromecast
I've spent years waiting for Google to get casting to work with smart TVs without a dongle, like Apple can do. It's clearly not a technical issue but a corporate direction issue.
And thanks for the pointer on lag on cheaper phones. She's currently got a low-end Motorola, so I shouldn't use that as a baseline. I'm going to try out the default "Dictate" on the Windows laptop tonight and see if it works, but need to remember I've got a cheap one and that might not show what it's actually capable of.