So If you put 1600A fuses in a 1600A fused disconnect switch it can carry 1280 Amps continuously.
but if you put in 1200A fuses that same 1600A switch can only carry 960A?
Yes for the fuse/switch combination.
You could put in dummy fuses and I think the switch itself wouldn't be harmed by carrying 1600A continuously, you just wouldn't have any OCPD. So it's all about what the fuse can handle in a particular thermal environment with sufficient confidence that it won't blow below its rating.
At least that is my understanding.
Cheers, Wayne
P.S. The document you referenced indicates that fuses are tested (in free air) to hold at 100% of their rating for up to 600A in size, and 110% of their rating for 601A and above. Which would suggest that for 601A fuses and above, even in a non-100% rated switch, it should be fine to run 110%/125% = 88% of their rating through them continuously. Except that there's no such provision in the NEC, and the 125% factor is somewhat arbitrary anyway, so there's no particular reason to expect it to work out like that.
I mean, I bet in 20C ambient the risk of ignoring the 125% factor for continuous loads on a breaker or fuse and getting an OCPD trip below the nominal OCPD rating is probably pretty low to begin with, since circuit breaker free air testing is done at 40C ambient, and I assume the same for fuses.