Your menus don't change because of the administrative overhead. In the mid-sized American city where I live, menus change seasonally at nice restaurants and daily at really nice restaurants. Even fast food chains experiment with adding new items all the time.
If you're able to change the menu daily, print the menus, walk through the menu with your FOH, then you can have an idea on allergens. Especially in those "really nice" restaurants where the attention is on the provenance of the ingredients (and changing daily because it was what was at the market that day).
It's just yet another arena where the US likes to wring its hands and make excuses for why the US can't do what all manner of other countries manage to do without issue, from things like this to mass transit to Internet connectivity to gun control to ... we're just soooooo unique that solutions that work elsewhere couldn't possibly work here.