Earlier quoted context omitted.
I really hope that sysadmins/people are not using the same private key for work and pleasure. And for that matter, the same key at work for DEV/TEST/PROD. But you're probably right that a lot of them are.
Depends how you look at it. I use my key pair as my digital identification, whether at work or at home. I only have the one set. That logic held up until now I suppose, with the leaking of private keys.
The reasoning is that it is far easier for me (or the entity, but that's a bit different) to delete one keyfile to sever access than it is for me to rekey everything else. I don't want access to things I'm not actively engaged with - compromises happen, even to engineers' laptops, and that conversation with former employers is too much like calling up your exes to tell them about a VD test result for my comfort.
As far as it being digital identification, lots of companies have IDs separate from your DL/passport. This is usually because the company ID provides access to something your other ID doesn't. Same principle.
[1] There are lots reasons to have lots of different keys, and only having one per entity is pretty rare for me.