There are currently a few big players in the App store market:
Apple - by far the largest
Blackberry
Google (via Android)
Palm
Currently 3 of these 4 only sell phones on one US carrier, with Blackberry selling on all US carriers. Verizon has basically taken away from its customers the hope of ever being able to activate an iPhone on their network and run the risk of Blackberry jumping ship.
I understand the business strategy behind this, but I think that Verizon is going completely against the grain and is unlikely to find success.
One thing to note is that customers would still be able to install another App store on the phone, it would just take another manual step that many customers won't know how to do.