But I'm afraid with the change to a big polar cap as we have now (remember it used to be islands of just polar), and the fact that all polar terrains gives water, and the high water of melting lenses, that allowing improvements on polar sink as well would make polar cap cities uncharacteristically better than cities elsewhere
I think the polar zone should be more water-rich, and valuable. The whole point of the polar zone was to create a valuable central area to fight over (king of the hill style) and to mimic the big economic value of the polar water resources.
If you're really bothered, I think the better solution is in tile yields, not improvement limiting.
You could change polar so that it was 1w, and polar sink was 1w1h, and then allow improvements to be built there as normal (cottages and solar farms).
I'd also be fine with removing the ability for non-ice resources to spawn in the polar area (though: either this or the yield changes, not both).
But the polar zone should be valuable. It already doesn't have any health resources (for water collectors) or food crops, luxuries, or mesa tiles. So the yields aren't that great. But with no improvement construction and the status quo, the area just isn't valuable enough. It isn't worth pushing to settle or claim it early or to focus war there.
The other option would be to reduce the cost and increase the effect of the polar water shipper buildings (that give water per ice resource).
you won't find any mention of settlements, nonetheless major cities there, and it was to my recollection only settled at all for the purpose of extracting polar ice
"There are other cities scattered in the northern regions of the planet (especially near the ice cap, where water is harvested)"
http://en.wikipedia.org/wiki/Arrakis#Other_locations
And also for Ahriman, while polar sink will be fairly slow to terraform, once it has, you will be able to build improvements on it.
... you should be able to build improvements on it *before* it terraforms. Sink terrain in the polar zone should be some of the best terrain on the planet. It should certainly be better than the non-sink terrain, because it is sheltered from the winds. The whole point of the sinks is that they are supposed to be superior, it is really weird if sinks are better on non-polar continents but sinks are worse in the polar zone.
Polar area should be useful for non-Paradise civs, and it should be useful to found cities there immediately, not only after many dozens of turns of terraforming.
I'm fine with the slower terraforming rate. I'm relatively indifferent to whether they start with moisture, or get it only from melting lenses and catchbasins/reservoirs (though of course it matter for more than terraforming, because it affects cottage yields).