The 4T65E definitely has a bad, and in my opinion, unwarranted reputation.
With the huuuuge number of these Impalas made and sold, you're going to get one or two bad transmissions. Add to that the fact that a lot of these Impalas were fleet / rental / commercial / government vehicles (especially considering that these types of vehicles are generally abused more and maintained less than a privately owned vehicle: you know what they say... the fastest car in the world is a rental) you're gonna get even more failures. Also, the 4T65E wasn't used in just a few makes or models. I believe the 4T65E was used in about 35 different makes and models at different ratios, and the 4T65EHD was used in 12 different makes and models at different ratios.
These all contribute to a very vocal minority. You won't hear people asking for advice on the internet, or complaining about a working transmission. As others have mentioned, as long as you maintain to some extent your transmission, these are probably not likely to fail.
There is one caveat though... which is the "slip bang" that can occur due to a failing pressure control solenoid, where if you accelerate from stop it seems like the transmission is slipping and then it goes into gear all of a sudden with a jerk. In my 2008, with 123+k miles, I do actually experience this issue. However, it is pretty rare. It only seems to occur under very specific external weather circumstances (how or why is quite beyond me). However, I must say, I have had this issue for over 30,000 miles and 99% of the time, the transmission works flawlessly. I know of Impalas with the "slip bang" whose transmissions never gave out over the course of 300,000 miles. It seems like this issue, while it could be a problem, doesn't necessarily kill a transmission wholesale.
TL;DR The 4T65E in my opinion doesn't deserve it's bad rep. With proper care, it's pretty reliable but does have one or two quirks.