First of all, here's my proposed markup for this. I think that this is lightweight (not taking up much space) compared to Spevacus's proposed markup, and is much easier to identify compared to the one proposed in user1306322's answer. It also helps better align with SE's brand guidelines. Here's how it would like for moderators:
...and for non-moderators:
Here's the HTML I used to create that box:
<span title="staff" class="bg-orange-400" style="border-radius:3px;"> </span>
Second, while I'm all for this indicator for the reasons put forth in the question, I do have one concern. The moderator diamond is applied to all places where the moderator's name is linked, even those that were made back when the user was not a moderator. This isn't that much of an issue, because 1. there's enough context, 2. they're still a volunteer and still acting in that capacity whether they're a moderator or not, and 3. new moderators are (usually) asked in questionnaires regarding their thoughts about a diamond being visible on all their prior contributions.
For staff, however, making it behave like the moderator diamond would be inappropriate. For once, many staff members have previously served as volunteers, and have made opinions on meta sites that are inconsistent with the current team consensus. I've seen at least one case where a staff member posted a comment in support of a feature request back before getting employed, only to later on decline that request. Additionally, it gets confusing to see posts written back when one was a staff member, only to get confused upon them not having the staff indicator (they're former staff).
Finally, even on meta sites and even if the user is a current employee, it can get confusing whether a user is acting in official capacity or as a volunteer (not only for posts, but also for moderator actions if a staff member is moderating a site through their spare time through their staff rights). (Wikipedia resolved this issue by having staff have separate work and non-work accounts: the work accounts would have "(WMF)" in the name and would be entitled to all staff rights, while the non-work accounts would be treated in the same way as other normal users.)
I'm therefore in support of Spevacus's proposed feature to allow staff to manually apply this indicator to given posts, but I'd also like to add one more thing: that this indicator also remain visible on posts made by former staff members if it was added at the time of posting. Also, the markup of the actual indicator should be per the mockups above.