This is actually not unique to Nightly - the stable build does it, too.

I do recognize that scheduling updates is hard - no user ever wants to stop what they're doing and restart something, and it's important to keep users from running problematically out of date software.

I agree with OP though that this particular interaction is unusually frustrating for me. This message only appears after trying to load a link or a new tab, meaning it's actively waiting for me to want to use the browser before telling me that I can't, essentially guaranteeing it will interrupt my workflow.

I don't have a good suggestion on how to fix this without making the update system less robust - it might just be a necessary evil - but I do feel that OP's concern is legitimate.