Re: "Cost" of switching
"the domain of their provider as opposed to web email"
They may well be using the web mail of their ISP but I know what you mean.
One reason for moving ISP not listed was the ISP being taken over, perhaps repeatedly with downward steps in customer service and service provision until, as happened to me, it ended up in the hands of an ISP whose name has a couple of Ts in it. At that point I realised it was a good idea to shift the email domain first and, rather than get to depend on a branded email provider*, get my own domain with a registrar who would also provide an email server. That made it easier to move ISP again.It also made it easier to move the domain registrar when they kept having a lot of outages.
So I now have ISP, email domain and MSP independent of each other. In addition it's possible to give different companies their own email address so you can see who leaks (hi there, eBay, hi there PayPal) and temporary addresses for one-offs.
It would have been easier to start off this way but otherwise you only have to bite the bullet of changing email addresses once.
* Actually it's just as well to have a free branded provider as well, even if it's only to provide cover whilst the MSP is being swapped or to give out to people you don't even want to go near your domain addresses.