Never gonna happen under normal usage of modern screens. Both of the example images in that article seem to be fairly old computer monitors, not TV sets.
You do need to be aware of the room when you’re making this decision. I replaced my cheapy LCD with a nice LG plasma, and reflections are much more (annoyingly) noticeable with the plasma - now, it’s important to make sure to close the drapes during the day if you want to watch TV, and the pole lamp beside the couch must be off. If the movie is dark, bright objects in the room can be distracting; I’ve changed my shirt a couple of times because it was too annoying.
This was never an issue with the cheap-o LCD - and it’s not a huge issue now - but I’ve got a darkly-coloured couch and walls, and it’s not hard to close the curtains, turn inconveniently-positioned lamps off, and (in rare situations) change into darker clothing. But if I were buying a new set, and I had a white sofa or a window opposite the television that wouldn’t benefit from dark curtains, I would rule plasma out.
The plasma also kicks out quite a bit of heat, so that’s something to consider, too - if you have any trouble keeping your space comfortably cool, you probably won’t want to add the extra heat to it.
That said, I do prefer the picture on my fancy-pants plasma to the cheap-o LCD, under the right conditions.
I disagree that the rainbow effect has been eliminated. Modern DLP projectors have a much faster color wheel, but it’s still a color wheel. I found older DLP setups virtually unwatchable, newer ones are better but I still can see it. But that raises a point, if you’re looking at a honking big TV, you should consider whether a projection setup is something your interested in. I fit mine in a normal sized living room; the 100" screen retracts behind the valence of a picture window, and the projector is on the lower shelf of a coffee table. The whole thing is much more unobtrusive than a 50+" TV would be