I think most everyone hit the major points, money, time, and fluidity. Supporting one console, and one console only means you save more money on hardware, and have more money to dedicate to the titles. Further more the costs compound if you plan to follow backward compatibility down the rabbit hole.
Who has the time to exceed a single console granted that the console is meeting your needs. Most great games can run between sixty to eighty hours. So one game should satisfy the average gamer between three to four weeks. With a decent library one should never run out, and with games with good online components eating hundreds of hours chances are you will never for an instant feel a lack. One console more then satisfies the need.
Finally fluidity which is the simple fact that you will gravitate towards one console to satisfy the vast majority of your needs. In the same way a person is right or left handed. You will find that one or more consoles will basically go unused, and that means they were poor uses of money and your time.
Will you miss a few games you want to play. Well honestly that only applies to the truly anal. The reality is that nobody gets worked up over missing a few games. Especially since you can get your hands on other good games that offset the loss. For instance there is a few games on platforms I do not own that I would like to play, but I am not losing any sleep over it, and it sure as hell isn't worth the cost of eight games to play one game. To me eight good games will more then sooth any feeling of loss. Which I just never have.
Buying and supporting multiple consoles is just a waste of money, time, and in the end doesn't have any reasonable benefit.