Keregioz
Kimon Zeliotis
I could say the same thing about guitars, pickups, amps, cabinets, and microphones - that doesn't change the fact that each one is a huge part of the cumulative tone.
I believe most of the things you mentioned have much more significant impact on the tone than what pick you use. It's more important HOW you use the pick.
Changing the pick changes a lot about the timbre of the guitar. As for you not having tuning issues... maybe you should pick harder.
Ι believe I pick hard enough, but I'm wondering, picking softer isn't in some ways the same thing as using a thinner pick? In both cases the result is less hitting power on the strings.