With every other change I make, I have to test in a dozen clients and make sure it looks fine. Why is there so much variation in email style implementation amongst different clients?

I've worked with people at companies where this was their only responsibility. Setting up emails for clients, making sure they pass a battery of tests and look great in all browsers and clients. It's an incredible PITA and it's not a set it and forget it thing. Clients can change month to month; spam filters change, etc...

There is a lot of variation in styling support among different mail clients

Email tools/clients are inconsistent in how they render HTML and CSS. A designed email might look great in Gmail, broken in Outlook, and unreadable in Apple Mail. Half of all emails are opened on mobile devices (according to one study). Email looks good in different clients? Great, now make it work on a 4" screen just as well as on a desktop.