I think about this often. Without smartphones, none of the problems we blame on social media would exist. We've gained a lot from the smartphone form factor (I haven't been lost in 10 years, for example), but whether we've lost more is a really open question, in my view.
This is a good solution and pretty much what I've done. When you need screen time on the go, putting those videos on an SD card and sticking it in a cheap Kindle Fire with VLC installed also works well.
I tried YouTube Kids, but found it was suggesting a lot of surprise egg and colorful slime videos. I blocked those channels, but more showed up, so I deleted the app.
Depends how old your kids are, but that's what I use it for. You can set the home screen to your subscription list, and it doesn't show related videos unless you go to a separate tab. Those two things have saved me from much screaming about not getting to watch the colorful slime videos that regular YouTube always suggests.
Carrying a smartphone is incompatible with privacy. Unfortunately, so is using a credit card (https://www.fastcompany.com/90490923/credit-card-companies-a...) and having a face (https://www.wired.com/story/get-used-to-face-recognition-in-...).
We're all doomed, so you may as well just use the software that makes you happy.