Running automatically that desktop issue.
If butler daemon and communication with it is required for launching games, that should do some itch application(or maybe even itch if that does not complicate so much and maybe patches are welcome) and try not have another user launcher with their own program communicating with butler(in docs there is saying only on windows?) and trying to guess where data are located and maybe be blocked by some itch development issue or progress or even operating system policy.
And butler also requires some info about launching with previous info get from it to post info how to launch it, so some desktop shortcuts seems cumbersome as program in the middle to have launcher for itch so bye bye common sense present in operating system... But if itch decide how to have this functionality then may be more desktop experience be in and also itch application have be the only point of itch development and user in.