Yeah, ours have had Fire Tabs. I feel way more comfortable with a $35 tablet (Black Friday/Prime Day price) in a toddlers hands than a $400+ iPad. Also, if you pay a little more for the 'Kids Edition' it comes with a nice protective case and lifetime warranty.
The case isn't a big deal as you can buy a similar one for <$10, but the warranty is great. Our daughter slammed hers to the ground in a fit of rage at her brother once when she was 2 and shattered the screen, and Amazon sent me a shipping label to return it and mailed the brand new replacement within a couple days.
Kids won't care about the lack of full HD and most kids' games don't require a ton of RAM, so I don't see a real reason to pay a lot for a spec'd out tablet for them. Also the Fire has an SD slot, so extra storage is dirt cheap and easy. You could even keep an extra or two pre-loaded with additional videos and just swap out. Though, in my experience, kids are likely to watch the same favorite video or two 1 billion times no matter how many options you give them.