So the thread title is this....
Is it okay for your story to not specify the settings?
It's you asking for feedback.
And if anyone cautions you or warns you about the possible pitfalls, you defend why it's okay.
Then why ask for feedback if you already got this covered and figured out?
Maybe next time entitle the thread
"I don't always specify my story's location. Anyone else do this?"
I agree with @tired_programmer if the story doesn't need it don't. If it does, do.
The most relevant reason to fill that information in is so that your audience can extrapolate the details you'd rather not mention. In other words, a small tid bit about the location can fill in what the houses look like, streets, what the laws are.
The geography.....population density...
Or, you can fill that in with accents, slang, names, etc....as you stated...so you're aware of how to fill in the gaps as the story moves forward.
It would be jarring id you didn't plan and just decided not to- because, you know, that's a thing and then decided for a plot point to land in a certain place that no reader was expecting. It would flip their entire perception.
You mentioned swampy woodsy bogs so we thought Florida....
And then you mention tropical birds in chapter 9.
And the final act is in an abandoned Disneyland with zombies with Aussie accents...."Brains....mate..."
But then they stumble out of the woods and there's a volcano.