Google's John Mueller said on Twitter that Google already can and does recognize broad site changes and thus there is no need for a button in Google Search Console to communicate these changes. John said "we already do that when we can recognize broader site changes -- no need to make a (potentially confusing) setting."
We already do that when we can recognize broader site changes -- no need to make a (potentially confusing) setting :)
— John ☆.o(≧▽≦)o.☆ (@JohnMu) July 17, 2018
This is in response to a webmaster asking for a way to "make URL transitions faster."
Google does have a change of address tool but this only covers specific cases. Simple URL changes is not covered here, using 301 redirects is the way Google typically suggests you go.
When Google does see massive URL changes on a site, it isn't uncommon to see Google increase crawl rates on the site to pick up on these changes faster and index those new signals sooner. But I hear, having a way for you to see Google actually does know about the change and that it is processing the change as you'd expect would be super cool. You can use reporting and analytics and log files but a simple notification from Google that this is what they have found and this is what they are doing would be sweet. How that would work can be complex and I assume there can be so many scenarios that this would be a complex task for Google to accomplish.
Forum discussion at Twitter.