As far as the movement is concerned, the hydraulic brake system is self-adjusting. So regardless of the thickness of the brake pads, lever initial position and lever travel will always be the same. That is, assuming that you have the original master and slave cylinders. If somebody messed with either, then the amount of fluid the master puts out might not be balanced with the amount of fluid the slave needs, and may affect lever travel. You may want to check the part numbers on master and slave cylinders to see if they're original.
As far as brakes fading or not, there are several types of brake pads available. The same applies to the rotors. There is no ideal material for all circumstances. Some rotors only perform when dry, others also have good performance when wet. Some brake pad material works reasonably well in all circumstances, other brake pad material might need a bit of heat build-up to work effectively. Those are great for racing, not so much for street use. My thinking is that the PO thought better than Suzuki and equipped your bike with racing rotors/pads instead of a combo for street use. See if you can find manufacturer and part numbers on the pads and discs, and what type of material they're made of. That may tell you whether what you describe is normal behaviour or not.
I was going to suggest you swap everything (all rotors and pads) for OEM, but I just bought that combo for the upcoming major service, and it's near 500 dollars or so, so not something to try as part of your initial troubleshooting efforts.
(Edited to add: The brake has been properly bled, not? If the brakes feel spongy, then there may be air in the system somewhere.)
Last edited by BackPacker; 03-20-2019 at 06:15 AM.