I don’t expect an accurate reading from a laptop charger. The current for that alone is almost certainly below the specified 10% - 120% flc where the c.t. accuracy is guaranteed, and the power factor and the shape of the current waveform is anybody’s bet.
But I would expect reasonably accurate readings from something like 2 A up to 100 A. Are you following the calibration procedure in ‘Learn’, and are you using the word “exponentially” in the figurative sense, or a strictly accurate engineering sense? Because I would expect any error, when you’ve calibrated at a sensible current for the c.t. rating (and I’d aim for 30 - 50 A) to be quite small between about 5 A and 100 A, and I’d expect it to increase outside those limits. At the top end, I’d expect the output to be low due to saturation, and at the bottom, it could go either way but I wouldn’t be surprised if it read high due to noise pickup. You haven’t yet said what hardware you’re using and running emonLib on, and that could be having a significant effect.
Whenever I’ve checked a c.t. and an emonTx against my true rms multimeter (after calibration of course), it’s been within the multimeter’s specified accuracy, so I’ve been unable to say with certainty that there is a linearity error.
You’re assuming your Kill-A-Watt is accurate. Have you any guarantee of that? The spec. that I’ve found says 2%, but whether that’s 2% of reading, or 2% of full scale, or 2% of reading + n digits (as one would expect for a digital meter), we don’t know.
Note that you can multiply your load by using a multi-turn primary winding for your c.t., e.g. your 9.5 A load with 4 turns through the c.t. will look like something close to 38 A.