Rogovsky coils aren't used too often for HV applications...in fact I don't recall that we've ever built one for the North American market. We have built a few 345 kV CTs with Linear Couplers.
In general, the one advantage of a Rogovsky coil to a normal CT is the fact that it doesn't saturate. Outside of that, there is no clear application advantage. Another might be that in theory, they should be cheaper to produce since they don't require a core, however, the pricing is more market driven than cost driven for these type devices. That would change if they started being used more. Also, there is potentially added cost due to the processing equipment mentioned below.
The disadvantages are that the output signal needs to be processed electronically (normally), which is another source for failure/mis-operation. Also, I don't quite believe in their use for metering applications (although some will tell you it works), especially for low current levels. They also can't drive very high burdens, so application considerations are a bit different than for normal CTS.
In my opinion, with the burdens of electronic relays all by being negligible, the main burden on the CT is now reduced to the leads alone.
In the IEEE world, C800 is the normal protection accuracy for HV units. The normal lead budens would rarely exceed 2 ohms. This means that at 2 ohms burden, the CTs would be roughly linear up to 80 times rated current. For most applications, this really ought to be way over what is really needed. For a 2000:5A C800 CT, that means that the CT will be "linear" up to 160 kA on the primary!