I think from looking at a limestone map of USA that what you want isn't completely impossible.
You could perhaps have a continent with a couple of big mountain ranges and a big syncline between them. At some time in the past the large plain between the mountains was under a shallow sea that deposited limestone. And while the mountains were the only things above the sea level, they would be eroding some. What you need is a reason that your limestone doesn't get buried beneath a thick layer of insoluble sediment.
So, other continents at the poles to give you a lot of water locked up there NOW so your karst is exposed. Sometime in the past that water was all melted to mostly flood the continent of interest and lay down a lot of limestone.
You need the climate across a large area to be the sort of thing that on earth happens in smaller areas. Across a range of temperatures. You might want to write in differences in different places. It wouldn't all look the same.
Your vast karsty stuff is temporary on a geological scale, but it might exist when your story needs it to.