You should also do it for purely selfish reasons. Chrome is sunsetting SHA-1 for use in certificate signatures, and Chrome will eventually show SHA-1 certificates as insecure.Referring specifically to this point, and not to your wider point about moving away from SHA-1, "because one browser maker said so" is rarely a good reason to do anything.
Google has an irritating habit of deciding it knows best for the entire world, but often it gets that call wrong and winds up degrading the experience for people who aren't in its chosen group of blessed users. The Firefox team are similarly arrogant at times.
However, in the real world, large organisations also use browsers to access intranet sites, and their requirements -- particularly with regards to security -- may be different to users surfing the public Web. Developers do need to do things with sites that aren't fully configured yet or are in transition from one system to another even if those things might not be a good idea when surfing the public Web. And so on.
So, I urge you to support good practices by making solid technical arguments for them. For example, in this case you could explain or link to information about why the SHA-1 issue matters for those who don't know. Please don't promote browser makers as authoritative sources of best practices instead, because often they aren't.