My DD watches some TV which I am perfectly happy about.
However just because we have a TV in the house and DD watches it doe snot stop her dpoing all the other stuff listed on this thread.
She has been capable of playing independetly from being tiny, happy to go off and play with Happyland from 2yo for example. Right now, at 7y, she is in her room. She is playing with Polly Pockey and some new Disney versions along the same line. Has been up there for over an hour lost in her game. Before that, before I went to doctors, she spent 45 minutes writing a story of her own.
Having TV about has never prevented my DD from doing anything else, and I have never felt the need to limit or restrict it particularly - well, other than Dh who will watch any old rubbish
Mind you, the fact that she doesn't seem to watch a huge amount of TV at home might be the reason why, on the flight to the US last week, she managed to sit for almost 7 hours watching a range of films and TV programmes, without even the need for a toilet break