I think that affinity was always there for me, but the first Star Fox game (and the accompanying comic that ran in Nintendo Power at the time), definitely woke me up to it.
It was years later before I found the fandom on the Internet and learned there was a name for it.
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wants to stop what they're doing and restart something, and it's important to keep users from running problematically out of date software.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.