I switched everything over to gmail at least a dozen years ago in anticipation of an eventual switch away from Rogers. It didn't end up happening until over a decade later, but forewarned is forearmed, etc.
It was far less painful than you'd think. Basically, just go through your list of important sites and services that you use your Rogers email for. On the first pass, you'll remember 80% of them. Over the next few weeks or so, you'll remember or run across more. Over a few months, max, you'll have a list of all of the important ones (if in 6 months, you don't remember or use one, you probably don't need it). At that point, you're prepped for a switchover.
There are so many carriers nowadays that are so much cheaper than Rogers or Bell too. I had stuck with Rogers because I could always get a screaming deal, usually by whispering the word 'TekSavvy' (or whoever the latest competitive threat to the Rogers/Bell hegemony was).