K=secret-key is no more a special value than K=11 (or 12 or 13 or any other specific value)
Agreed, but the difference is that to recognize values k=11, 12 ... you need a lookup table on the r value that does not worth it! Checking r=Qx is at no cost!
To recognize K=11 you do a comparison with a constant. To recognize K=secret key you do a comparison with a dynamic value. In either case the operation is the same and you only recognize one possible K. Maybe you can argue that you save a word of memory, but this is a trivial cost.