Does the US allow emergency medical evacuation of COVID-19 positive individuals for financial reasons?

Is the US government likely to approve medical evacuation by air back to the US under such circumstances?

Medical evacuations do happen but they can be expensive (hundreds of thousands of dollars wouldn't be uncommon for an evacuation by air ambulance). CNBC had an article about this in April:

The Centers for Disease Control and Prevention require air passengers to present a negative Covid test (or proof of recovery) before entering the United States.

“Extremely limited” exemptions are allowed for emergency travel, according to the CDC’s website.

Covac Global’s services fit this exception, said Thompson, adding that the company has never been precluded from bringing a member home. Medical travel must be via certified air ambulance, under the care and recommendation of a physician, and detailed paperwork must be filed with the CDC, U.S. Department of State and Department of Homeland Security.

“This is the only way a positive Covid-19 patient can enter the U.S.,” said Thompson. “We have had many people call up if a charter or even their own aircraft will be able to bring them home, and the answer is no.”

So while they are likely to approve medical evacuations, that likely means that you do need an air ambulance service rather than a regular flight (or even your own private plane).

To expand on @JJJ's answer, there are four possible scenarios post-infection:

1. You recover at home or after a brief stay in the local hospital. Assuming you're fully vaccinated, under the age of 65 and have no major pre-existing conditions, the odds of this are around 99.9%.
2. You take a long time to recover but can at least survive without supplemental oxygen, while also testing negative for COVID. In this case you just hop on a plane (in a wheelchair if you have to) and go back home unassisted. This will be the case for the vast majority of people who won't fall into category #1.
3. Your condition is so bad that you need a constant supply of oxygen and a doctor by your side. This will definitely require a medevac flight which will be very expensive.
4. Your condition isn't too bad but you keep testing positive for COVID for months in a row. This can happen but is extremely unlikely, otherwise we would constantly hear about such cases. If you do become the 1 in a million case where this occurs, you would likewise need a medevac flight to get you home, possibly a bit cheaper since you won't require active care. Interestingly, Dutch rules have a special exception for that allowing you to travel home with proof of that situation, see Positief blijven testen na coronabesmetting here, but not the US (thanks, @JJJ)

Overall your odds of needing a medevac flight due to COVID alone are very much negligible as a vaccinated person. I'd be much more worried about getting into a car accident during my stay than about getting infected with COVID. If you weren't worried about getting the flu during your travels in 2019, there's zero reason for you to worry about COVID in 2021 (post-vaccination).