I think this is ultimately just a "idioms I don't like" video. If she presented it as that, then fine. I completely disagree with her rationales about not using most of them.
'Piece of cake' is extremely common in current AmE. In fact, it's one I teach to my students.
I selected the ones I teach based on how common I think they are, or how likely students are to hear them, especially in our general area. 'Piece of cake' is on my list for that very reason.
I see at least one YouTube comment stating that they found several on her list common in their area. I think she's maybe also confusing "not widely used in my local area" with "not widely used across the US".
'Tickled pink' and 'chew the fat' are quite common locally as well, and both are on my teaching list.
I imagine she'd really object to our regional version of 'raining cats and dogs' - we frequently 'raining like a cow pissing on a flat rock'. The opposite of course is 'drier than a popcorn fart'.
I think she just posting "I'm attractive, so accept everything I say as gospel' videos.