Edit: This isn't a total cost analysis, just labor like the person asked.
Then again, with the people to move the samples around (process and sort mail), clean/sterilize testing materials after testing, and manage the people that perform the tests, and do quality testing, you might see another $1-$2 per test in labor costs. So maybe $5 in labor all said?
My bet is that the most expensive part of the process is the machines to do the tests, which likely cost multiples of a lab tech's salary (but maybe can do multiple tests at once? I dunno).
A sibling comment upthread noted that Maryland got 500k tests for $18 each, which sounds like it's probably close to cost, if it's the same test. That number of tests would be about full time work for 400 lab technicians for 5 days if they averaged just under two minutes a test.
The other labor was really just going by your own numbers.
Beyond that, there's still the layers of management above, that while there are physically less of them likely, their pay scales higher as well.
Even if the virus is viable, it's no longer airborne. You'd have to touch the swab and bring it to your face. Most of these labs handle things like HIV, so lab procedures and training guard against this sort of behavior. I wouldn't be surprised if they worked with shields as well.
In short, maybe they should be paid more, but it's not the danger factor that should govern in this particular case.
In case people forgot the first step of the FDA was to shut down at home testing. Then they fast tracked Roche and Thermo Fischer.
Now a month later they approve an expensive at home testing kit. You take your own conclusions of this behaviour.
https://techcrunch.com/2020/03/23/updated-fda-covid-19-testi...
The LabCorp test uses a swab that doesn't go anywhere near as deep (2). For a test kit to be widely distributed, you need to have it be drop dead simple to run perfectly.
Given all this, I'm not sure we should jump to corruption as the reason this is the first at-home test.
1.) https://slate.com/technology/2020/04/coronavirus-testing-fal...
2.) https://www.fiercebiotech.com/medtech/labcorp-s-at-home-coro...