Until healthcare workers aren't complaining about not having enough PPE to do their jobs safely, this is the correct line of thinking, zero sum or not.
Personally, given the vastly greater risk of exposure for them, I don't think it's a zero-sum game at all, which is precisely why all available supplies should go to them first.
I guess I'm not convinced that the 10th one shouldn't go to them too. They are dealing with a vastly increased risk of exposure than I am, and likely with significantly greater infectious loads as well, which may^[1] increase the severity of the disease.
If for some reason I had to spend a lot of time in close proximity to other people, that might merit a homemade mask, but otherwise I think I'd be doing a far better job protecting both of us and everyone else we interact with (in the process of obtaining food and essential supplies) by giving it to my wife before she heads out for her next shift at the hospital.
Firstly, if everyone does this, there's 10% fewer masks for doctors than there'd be otherwise. I would posit that their need is so much drastically greater that they really should get every last one.
Remember—your job is to stay six feet away from everyone else, on the off chance they might have the Coranavirus. Doctors and nurses are getting up close with people they know for sure have the Coronavirus, all day, every day.
But more importantly, the masks are disposable! It's not like you can keep one and use it indefinitely.
It defies common sense to not wear a personal mask. Like donating your six shooter to an outgunned military. The marginal benefit to you is so much more than the marginal benefit to them.
More like donating your ballistic vest to a military that's expected to win eventually but with heavy losses. The marginal benefit may be low due to the sheer scale of the problem they're facing, but it still might save a life—and what if every American made a mask and donated it instead of wearing it themselves?
It's also possible—likely, even—that the severity of the disease in an individual is correlated with the magnitude of the initial infectious dose, and healthcare workers without effective PPE are going to be most at risk for high doses, which will act as a multiplier on the benefits of PPE usage for them. In the analogy, one might compare this to the chance that a stray, tumbling bullet fired in a high arc by the enemy will hit you while you're trying to buy groceries, vs. the chance that a soldier on the front lines will be lethally wounded by a deliberate shot. Who needs the vest more?
As noted here^[1], this is all very much up in the air, but the more I think about it, the more my brain rejects the marginal benefit argument as an illusion. Healthcare workers are on the front lines, and by most accounts it's their labors that'll cut the mortality rate from 10+% to ~1-5%. They need all the help they can get, and the rest of us need them to stay healthy and able to do their jobs.
Personally, given the vastly greater risk of exposure for them, I don't think it's a zero-sum game at all, which is precisely why all available supplies should go to them first.