The frustration of inaccessible accessibility

One of the best experiences you can come across when traveling is accessibility where you might not necessary expect it.
Of course finding inaccessibility where you would expect it to be is a drag.
But there's a third category that I think is as frustrating or maybe a little more so than the second. That's where there's accessibility but it's just not accessible.
Let me explain.
The best example I can think of happened to us when we were visiting New York City as a family vacation trip a few summers back. We stayed in New Jersey and took the train into Manhattan. A great trip that the kids and my wife and I still have many memories. Frolicking penguins and polar bears in the Central Park Zoo, a great water tour including a waterside view of the Statute of Liberty, being immersed in the iconic Times Square and an extremely filling lunch  at the Carnegie Deli (see photo below).
At the end of the day we headed back to our hotel. Our  kids are swimming maniacs, so after dinner there was an obligatory dip.
The indoor pool was down a few steps, but no problem since the hotel had had the foresight to install a wheelchair lift. But when we went to use it, we found it locked. That meant a trip out to the lobby and cooling our heels waiting for someone to unlock it.
I asked about why the lock, and was told it was to keep people from using it who didn't need it. You know, joy riding kids.
Yeah but the problem with that position is that it kept us from using the equipment too, even though we had a bona fide legitimate wheelchair user in our party.
It didn't ruin the day (see joyous photo above of the three kids), but it was frustrating. This hotel had had the foresight to install equipment that made the pool area fully accessible despite the stairs. and then they basically eliminated that plus by locking it away.
You really shouldn't have to fetch someone just to get into the pool if you can't use the stairs. This hotel didn't make people prove they need to use the elevator. (and as a kid I had played in more than one hotel elevator) Why should there have to be a disability test to use the pool area lift?
If you ever find something like this, let the person in charge know why inaccessible accessibility is misguided. And if you're in the position of opening up accessibility at a tourist attraction, lodging or restaurant, remember that the key part to accessibility is accessibility all the time.

Photos: Top , the kids in aforementioned New Jersey hotel. Despite the hitch getting in, a good time was had by all. Bottom, some of our food from the Carnegie Deli. The sandwich shown is just half of my oldest daughter's salami and cheese. The slab of cheese cake shown my son pretty much polished off on his own.