My daughter has had a kindle fire for going on 5 years now. I wouldn't part with it, but I know I'm likely in the minority. She uses an iPad at grandma's, but it's a distant 2nd place for us.
I'm sure there are apps available on other devices that are comparable, but we've been very happy with Kindle free time. $5/mo, and she gets unlimited age-appropriate games, streaming video and books. I set it for daily on/off times, maximum number of hours each day (with separate weekday/weekend options), as well as a reading/learning goals that must be met before accessing other content.
Password protected, so I don't worry about her accessing the internet or apps outside of Free Time. But you can import other content to the child's profile if you want to give them access (we did that with a math app she uses for school). She doesn't get a lot of video time, but there are a couple of
Amazon original shows she really loves, and the classic PBS shows are big hits in our house, too.
The free time apps can chew up memory quick, though. It's necessary to check their profile and delete some from time to time. My DD used to get a little carried away downloading games. It was a bigger problem on our first kindle (no expandable memory). It's less of a problem on the newer ones.
I use a kindle as well at home & at work. For what I need, it gets the job done as well as my co-workers more expensive tablets. There's pros & cons to it- it depends on what you are hoping to accomplish with it, of course. I just thought I would share our experience with it.