Should the TV go above the fireplace?
Not if you can help it, but here's what to do if you can't. I admit to absolutely hating the current trend of placing TV niches above the fireplace. Hate it, hate it, hate it. But if you are stuck and that's the only place your TV can go, put the TV on a wall mount or stand that will let you angle the screen down. That's because the screen is best viewed straight on rather than from an angle.
If you are remodeling or building and still feel you must put your TV above the fireplace, consider a narrow, rectangular fireplace placed very near the floor, like the one in the photo above. It will allow you to have lower and much better placement than putting your TV above a tall fireplace with a high mantel.