In a nutshell, the main problem with the Edge plan is that you're paying for your phone twice. Once in the additional monthly payments you make. And once by paying the same monthly price for your plan that people with subsidized phones pay.
If Verizon were to take away the monthly subsidy, then it might make sense to make additional payments for your phone (like T-Mobile does).
There is no way not to pay the same monthly fee as everyone else on Verizon even if you do buy your phone outright. That's why it was always better to get a subsidized phone on Verizon. Now that unlimited data is no longer an option, people are trying to find ways to afford a new phone, and stay on Verizon.
See: Moto X
Still, you pay the same monthly fee. It's like you are paying extra just to stay on Verizon.