The effects of testosterone are far from as simple as you suggest. It tends to lead to higher competitiveness. This is not quite the same as recklessness.
Meanwhile during normal usage the driver (of whatever gender) is likely to be getting shot at. This will tend to have a larger affect than their gender.
Yes, and millions of young men in the US who are shorter than millions of young women. What’s your point? Young men are still disproportionately more likely to be in road traffic accidents.
Re testosterone, the keywords you should be searching for are “risk taking behaviour”.
I’m curious also what percentage of time you think the average military driver is being shot at is.
And in the military, given how e.g. the draft has never applied to women. Times are changing, but very, very slowly, and there will always be a gender disparity due to physical differences (e.g. strength, see also: almost every sport)
Or to make a summery of the summery of the study: there is an association of risk aversion when going from low levels of testosterone to very low levels, but "male with high testosterone" is not supported in that study as increased risk taking behavior vs males with normal levels of testosterone.
No -- being shot at is 0-2% of your time deployed. The rest is waiting around.