She was so focussed on it and started crying when we hid it after only a very short time. This is not normal a behaviour. This only happens with things that are very addictive (also for example sugar). I do understand that not everybody can do it like that, but if you can create such an environment it's much better for them (in my opinion).
>> started crying when we hid it after only a very short time
I'd cry too if you showed me a bright colorful shiny fun new thing and then took it away after only two minutes.
Part of what you're seeing is the novelty. There does seem to be something about screens, but it's possible to have healthy screen habits as a young child. My 3 year old enjoyed a 25-minute episode of Wild Kratts on PBS Kids on our TV while we finished packing up for a trip to the aquarium today. No problems turning it off once the episode was over and it was time to go. It's not his first time watching TV though.
My approach to these kinds of things is different: these are really important opportunities to teach moderation and to teach the social skills of learning to have fun things in moderation.
I think it's quite important to introduce these addictive things into their lives, in a way that teach how to enjoy them carefully and in small chunks.
My three year old would do the same thing if he was playing in his sandbox and I abruptly picked him up and carried him away from what he was doing though. In my experience managing transitions between activities is one of the most important things. If I let my him watch a video and I tell him "I'm going to turn off the TV when it ends", he just goes back to playing with his toys when it goes off.
Don't get me wrong, I think screen time can definitely be a problem. I just think it mostly comes down to whether or not the screen time is at the expense of something else more constructive.