Depends on the level of compromise. If an attacker can interface to the screen and keyboard, or access other process's memory to directly read the key from there, or spoof the SSL library so you get cleartext network transmissions, sure, they can steal a lot of data.
But if the attacker only has access to the filesystem, then it certainly matters whether the filesystem contains enough information to impersonate a user.
And there are things that people do to desktops that allow other people to access their filesystems. Things like cloud backup, sending your computer in for repairs, or selling an old hard drive. Sure, you should remove the hard drive or wipe it before you do any of these things, but a lot of people...don't. There are plenty of stories about that situation floating around the interwebs, but this comment is long enough...
But if the attacker only has access to the filesystem, then it certainly matters whether the filesystem contains enough information to impersonate a user.
And there are things that people do to desktops that allow other people to access their filesystems. Things like cloud backup, sending your computer in for repairs, or selling an old hard drive. Sure, you should remove the hard drive or wipe it before you do any of these things, but a lot of people...don't. There are plenty of stories about that situation floating around the interwebs, but this comment is long enough...