You are right, I could have been more specific, they do often care about maintaining control of their account. I don't think they care very much about their message history though, and there is at least some segment of the population that considers email accounts entirely disposable.
You'd be surprised about the number of emails I've received from people who apparently don't care about their email/website asking if it was vulnerable to the heartbleed/heartbug/heartbeetle/heartblood malware/virus/bug/issue/exploit in the past week.
Though I must say I find it funny all the different names/what exactly it is I've seen.
