I've got a few issues with L2s around me. A few that were originally listed as public seem to have disappeared from apps and such and now are either private or just not listed. I've also seen a few break and no one ever fix them, to your point, these are places that have at least at some point advertised how they're reducing their footprint and supporting green tech.
Are you talking about the PlugShare listing? That's crowd-sourced data, so an initial "public" listing that changes to a "private" one might simply reflect an error in the initial entry creation. The site owner might not have clearly marked the EVSE as being private, or the person who created the entry might have overlooked the relevant signage. None of this has anything to do with the carbon footprint, except indirectly or in conjunction with other factors. If an EVSE is reserved for, say, employees of a business, then other people won't be able to use it; but they'll still charge elsewhere, so it's a wash. That said, a private EVSE might do less to encourage EV adoption than a public one; and if a driver is forced to charge on an EVSE that uses the grid mix rather than one powered by 100% renewable sources, there'd be an impact. EV owners who want to minimize their own carbon footprint can often pay for a 100% renewable energy plan, even without putting solar panels on their roofs. For instance, in Massachusetts and Rhode Island, people can sign up with
Green Energy Consumers Alliance for electricity to get 100% wind power. (That's on paper, of course; it doesn't change the physics of how electricity is delivered -- but it does change the economics of it.)
I've also had horrible luck with payments and now more often just insane payments. I'm not going to pay $3 to connect + $0.20/kWh or something for a short two hour visit on a 6.6kW charger. These either need to get completely absorbed by a big network that rolls out a single level pricing plan with no connection fees or something, but some of the prices are crazy if you think about 6 to 12 kWh being used...
If a business wants to cover costs, much less earn a profit, on public charging, then the prices charged will likely be greater than those you'd pay to charge at home, simply because the costs of installing and maintaining the EVSE will have to be covered. Lucky people will already have a 240v outlet at home and be able to charge with the EVSE that comes with the car for no extra hardware costs; and even people who need to install an EVSE at home will likely do so, regardless of local Level 2 EVSE availability, so factoring in the home EVSE's cost is inappropriate. At the moment, public EVSEs are sometimes (but not always) subsidized, either by businesses that hope to attract customers or by governments that hope to spur EV adoption. If the most convenient local EVSEs for you charge more than you'd pay for electricity at home, then the solution is obvious: Don't use them. If you're driving a Tesla, which is likely given this forum, then you have enough range that a short Level 2 charge locally won't make a difference to you.
Things get trickier for people who can't charge at home, of course, such as most apartment-dwellers. For them, the best Level 2 solutions are to have EVSEs installed at their apartments or at their workplaces. These might well be the private EVSEs you complained about earlier, and making them private is sensible because they'd be
needed by the residents or employees who use them. Local DC fast charging at supermarkets, restaurants, or malls could also help people who can't charge at home, but the higher costs of DC fast charging make this solution worse than Level 2 charging at apartments and workplaces, IMHO. In any of these cases, if the site host doesn't subsidize the cost at least a little (say, by charging local electricity rates and swallowing the cost of EVSE installation), then the apartment-dwelling EV driver is likely to pay more to drive an EV than would somebody who lives in a house. (Factoring in the cost of installing an EVSE for the homeowner is fair for this comparison, though, which complicates the comparison.)