Practically any adult around where I live could have got their shots already if they really wanted to. No one checks anything but your ID. If you say you have asthma or whatever, it's not like they would verify it. Still you might have had to drive out to a more rural area if you wanted it sooner.
I'm guessing the vaccine uptake rate is pretty abysmal if they keep moving up phases and have places calling people who were previously scheduled for later dates to come in ASAP if they can so they don't waste shots.
There are a few components to this.
One of the problem is that people got on multiple lists, rightfully so, which then created a longer wait list than there really was. I read that when Wake Co. did a scrub of their list, an absurd amount of the list had people that had already gotten their shot elsewhere so they opened up the list to phases earlier.
Two is that the supply has increased dramatically over the past month.
3rd is that in some areas, like you said, the uptake isn't great.
According to the states dashboard, of people 18+ of age, 34% are partially vaccinated and 20% are fully vaccinated, so 54% of all adults in NC have at least gotten 1 shot, and that's before they opened it up to everyone. That doesn't seem like an abysmal uptake rate to me, but it's hard to tell (and I'm sure it varies by county/demographics).