It's not that onerous if you've gotten used to staging your food handling. You just prep everything else, handle the chicken, set aside in a dedicated bowl, then wash your hands and go back to handling everything else.

Once I'm cooking, I just use a dedicated pair of steel tongs for moving chicken around, then I don't have to keep washing my hands, I just clean that set of utensils once I have a moment.

I think it's still worth the effort, it's just some specific food handling practices. After all, it's not like I don't practice the same caution when I'm handling any meat, and even for any other meat I'd have to wash my hands when moving from handling meat to veggies.