If people truly were making $3.37/hour full-time I think you would see very few drivers; it's grossly misleading to assume so many people aren't capable of managing finances. It looks like the full paper itself is currently embargoed so it's hard to examine the methodology. However, just looking at the math (assuming I did it right) it seems the conclusion are misleading (the numbers themselves indicate they probably just sampled all ride-share drivers throughout the US rather than full-time ones):

revenue: $0.59/mile
cost: $0.3/mile
monthly profit: $661
Average fuel consumption is ~26.4 mpg so let's round to 25mpg
Average fuel cost: $2.5/gallon
Average number of working days/month: 21.75
Average number of weekend days/month: 8.65

0.59 * x - 0.3 * x = 661
0.29 * x = 661

x = 2279 miles

2279 miles/22 days = 103 miles.
2279 miles/8.65 days = 263 miles
2279 miles * 0.59 = $1344/month in income or $16128/year.
2279 miles * 0.3 = $683/month in expenses ($273/month in insurance, maintenance & repairs, $273/month in fuel, & $136/month in depreciation).
. Average fuel price is $2.5.

2279 miles/25mpg = ~91 gallons. 91 gallons * 2.5 = 227/month in fuel.

Where it gets tricky is we don't have data on the average speed of an Uber driver & whether the 103 miles includes driving around waiting for rides. Let's assume a conservative average speed of 40mph.

103 miles/day / 40 mph = 2.5 hours/working day/month.
263 miles/day / 40 mph = 6.575 hours/weekend/month.

The faster you drive the less you work so if my average speed of 40mph is too conservative, then the average driver drives even less. It seems like this builds an average profile of a driver is one who picks up a rider or 2 on their way to/from their main job & then picks up some extra cash driving a bit on the weekend. The average driver probably doesn't consider Uber as their sole source of income but rather as extra income their making when they otherwise wouldn't be doing anything. Now of course that's probably less money per hour than they could pick up from picking up additional hours somewhere or even something like Task Rabbit. However the average Uber driver probably sees it as more reliable in terms of total revenue than Task Rabbit, it requires minimal effort, & it has extreme time flexibility that a second job wouldn't (just turn on the app whenever you want to make money).

Anecdotally the full time drivers I've asked in LA & the Bay Area told me they're pulling in 60-120k depending on how many hours they put in & the area they drive in. I didn't know this but apparently Uber & Lyft offer a lot of incentive programs that only the most active drivers can t take advantage of that significantly bumps your income (trips/day, trips/week, miles driven, etc). If you're not doing it full time then you're not getting these bonuses which is going to further impact your $/mile (of course I suspect the fares & costs are higher in these areas too). Since 40% of your cost is fuel consumption, drivers doing this full-time are going to prefer fuel-efficient, cheap cars than the average driver doing this on the side. This is obviously a more complete picture than the misleading news reporting might indicate.

*EDIT: As another comment pointed out, the cost numbers are artificially inflated. They're attributing to the entire cost of insurance to driving whereas from the model above the average driver already has a car. Thus they need to actually use the fractional increase in the more expensive insurance they need for the ride share vs what they would get otherwise. I suspect the same problem applies for depreciation where they're not using the fractional increase of depreciation cost due to driving more but just the overall vehicle depreciation which was going to happen anyway. Even the full time drivers probably would have bought vehicles anyway so the depreciation & insurance cost isn't reflective of that anyway.

TLDR: The main problem of the "study" can be summed up as follows: they take income from those who do it occasionally & subtract the costs of the ones who do it full time. Given the threat ride sharing poses to personal car ownership, it's not surprising such a misleading study is sponsored by people who would be impacted by reduced car ownership.