It would be GREAT to have a pickup there if you need something immediately. Or at least as soon as it gets there to the center.
I will suggest it to them!
Just saying that actually Amazon does have this option I was suggesting and it's already happening in Seattle. It's in this NY Times article below...
O ye of little faith! 
https://www.nytimes.com/2018/09/23/technology/amazon-seattle-testing.html
It doesn't mention anything about being able to get your items immediately. I just don't see how picking up at a center is preferable to having something delivered to your door.
I suppose, in theory, if you are really desperate for an item and are willing to go to the distribution center to get it, you might get your item a few hours before a delivery person is able to drop it at your door. But...in NYC where most don't have cars, and people are generally working during the day, how is this really beneficial to most people? If they ever do start this service, I can't imagine that I would ever want or need to use it. Seems like a time waster instead of a time saver.
The article mentions that such centers are popular in college areas where people don't have the luxury of being able to get their package dropped at their door. I guess for people like that, it makes sense. But I have a great UPS guy who comes to my building every day and drops packages right in front of my apartment door, and you can't beat that!

But yes, you were right that the option exists.