Actually, speakers for the overflow is a good idea. I don't think that a TV is really needed, when we know how to follow along in a missal, or not even follow along. We can tell by the words being said by the priest as to where he is in the course of Mass. Maybe, for newbies to the TLM, a TV is helpful, but they really shouldn't be the basis for a norm.
I have a TV and watch occasionally, but it would be better if I didn't. I mostly watch old movies and Hallmark-type stuff.
I recently read an article about the problem with TV. It's not only that so much programing contains bad things, but that most TV shows don't depict the fact that many Americans still have some sort of religious beliefs. On TV, the characters almost never have any religious beliefs, and that does not represent the reality for many people. But still we want to watch TV. I think it's a way to de-stress and forget about real life. But it can also move us away from growing in holiness, if we depend on it. It can be the same with the computer, though we can better control what we view on a computer. Just my 2 cents worth.
From the point of view of a mother, if you are nursing or have unruly children then a screen is helpful to see where you are in the Mass and help give some instruction to your children without bothering others. I spent 8 years in such a room and I am very grateful to its utility.