letz see, currently I have a pr
of Trek , Specialized (gel i think), Fox and a cheapy pr
of Saranac Gel bought at Big5 (CA lowlevel sporting goods store).
All have been through the wash (machine - delicate cycle with the rest of the cycle kit) at least 5 - 6 times. All come outta the wash in great shape, clean and not 'stiff'. All have leather palms and bodies.
I wouldn;t have done that some decades back, but the stuff they use now seems to standup well to machine wash and drying.
Only thing special I do is close the velcro clasp and 'pin' them with a safety pin soz they stay closed and the velcro doesn't 'rash' any of the shorts or jerseys.
After a few washes I will treat the leather with a quick, light application of Lexol to keep it well conditioned. A good quality hand lotion will also do that.
This may work for you, and again, it may not
you makes your choices and takes your chances.