I have noticed that many mathematics departments (a little over half of the public and private Group I departments) follow the email@example.com format. Does anyone know of a reference to a discussion in Notices of the American Mathematical Society or elsewhere about this common practice?
I don't have a reference about this. The split in email addresses is often because mathematics departments were among the early adopters of computing. I don't know whether this applies to your own institution, but it applies to several I have been at, of different sizes from 5,000 to 50,000 students.
When computing technology began to be available, mathematics departments were among the first adopters. Computers and mathematics go together. At quite a few schools, the computer science department is still part of the department of mathematics; at others, the two departments started together (when the math department began to hire computer scientists), and split apart later.
In the period before PCs became ubiquitous in the 1990s, mathematics departments often found funds (often via grants) to operate computer labs, web servers, and email servers on their own. At this time, especially in the 1980s, university-wide computing services were often quite primitive, and often consisted of terminal servers instead of PCs.
Over time, as computing became ubiquitous, universities hired their own IT staff, and began to run their own web servers and email. This is how, at several institutions I have been at, I had two different email addresses (one for the university and one for the math department) and two web pages (same split)
Now that email and web servers are viewed as a basic service that the university provides to faculty, it is more difficult for mathematics departments to justify having their independent systems. Administrators correctly look at the separation as an inefficiency, asking why the department can't use the same system as everyone else.
In my opinion, math departments that want to continue to have separate systems will need to present a very strong case for why the separate systems are necessary, beyond the historical developments that led to the separate systems coming into existence. As email and web services become more and more of a staple commodity, this argument gets more and more difficult.