BJC-
A few points.
As davidbeach correctly points out, protection accuracy is basically a statement of how much voltage the CT can develop on the secondary without saturating. A CT rated C400 can develop up to 400V on the secondary without saturating (not exactly the whole story, but good enough for this discussion).
Look back at the diagram, if each CT develops 400V across its secondary and the CTs are connected in series, then 800V is developed across the pair. Hence the C800 rating as a pair.
"You might get a greater burden but if you connect two 800:5 cts in series and run 800 amps through the primary you won't get 10 amps out of it."
Remember a CT is effectively a constant current source. The burden rating is not related to the current being put out of the secondary at even given time, i.e. a unit rated with twice the burden rating, doesn't put out twice the secondary current....it puts out twice the secondary voltage, or rather can be pushed up to twice the secondary voltage.
"I think it's just a connection to mitigate the effects of a spare transformer. If you have a spare on the bushing of a breaker you can't leave it open and if you short is it just gets hot."
I very much doubt this is the case and if it is, it is a very poor practice. The heat developed in the second CT is essentially the same whether it's shorted or has a burden connected to it. The heat generated in a CT is dominated by the I^2R losses in the secondary. Technically, a CT with a burden across it will generate slightly more heat, as the cores losses will be higher, i.e. operating at a higher flux density.