Yes, that’s how I assumed it too. Which is exactly why saying that Shuster used the skylines of Toronto or Cleveland in his drawings is such a bad answer. I went through early issues looking for clues about the city in the comics since people kept making a big deal of that. But there simply aren’t any. The very early Superman existed in a nebulous non-world that didn’t correspond to anything. It was only with time that Metropolis became an obvious analog to New York, and Gotham City also became one. They were both the biggest and most important, full of stuff that villains-might-want and artists-could-use, cities in the country simultaneously.
DC has never canonically put their cities anywhere. John Byrne famously put Gotham City in Delaware and DC has spent a quarter century trying to erase that from people’s memories because of the embarrassment. Every retcon and every new set of editors and every remake wipes out the past and plays with the mythos. Flash ostentatiously lived in a blue-collar city for one recent incarnation. They said that over and over but I still don’t know what exactly that was supposed to mean. Coast City was obviously on the West Coast, but they thought so little of it that they destroyed the city entirely. True, they also destroyed Gotham City entirely once but they brought that back almost overnight when the arc was done.
Marvel treats New York like a semi-real place. DC treats its cities like Epcot. They are backdrops for whatever attitudes they want to project. I mean, Nighthawk went off to a place called Blüdhaven. Give me a metaphorical frickin’ break. And, you guessed it, they destroyed Blüdhaven too.
DC cities aren’t analogues of anything, and today they aren’t thinly-concealed anything. They’re painted backdrops. Which you can argue is what they should be. Marvel finally decided they had to deal with New York getting hammered by a zillion alien evil doers and they never really recovered from that. They now - occasionally, when they remember or it’s important to the plot - try to make the death and suffering real - and it just feels more fake than the superhero physics. At least DC can pretend it’s just a comic book city.