You are not alone. Transport for London found safety concerns as the biggest reason people do not cycle in London. Interestingly, many people who do cycle also considered it too dangerous.

For what it's worth, your risk from diseases of inactivity (diabetes, heart disease, etc) are far greater than the risk of cycling, even with poor infrastructure. Most people who take up cycling to work see an increase in life expectancy.

The solution is to separate cyclists from motor traffic on all major roads and introduce 30kmph limits on quiet roads. The Netherlands did this and has far lower accident rates, despite having more children and elderly people cycling. They don't wear helmets either!

I would assume cycling safety increases proportionally with bike infrastructure. Something tells me the people dying on bicycles aren't dying from collisions with other bicyclists. If you have adequate infrastructure bike safety starts to become a marginal concern.

I grew up trained at school to always put on a helmet else I'd end up a vegetable after a bike accident. Not one mention of how American roads are designed for car supremacy at the expense of human safety. A helmet won't do you much good if a texting SUV driver hits you.

Meanwhile in Europe barely anyone wears helmets. It turns out you don't need them when bikes have their own dedicated infrastructure.

Motor vehicles aren't the only risk; whether a helmet would prevent serious injury in an accident depends on factors such as how fast you're travelling, and you don't need to be sliding along the ground too fast and connecting with a a kerb/a wall/street furniture for a head impact to cause life-changing injuries.

So I've been biking most of my life and I almost never wear a helmet. Not because I don't think they would help if I hit my head on the ground, but because in the past 20 years I haven't been injured while biking once. Maybe I'm just lucky, but I think 99% of it is just being cautious and aware of my surroundings while riding. At this point riding without a helmet is simply a risk I'm willing to accept.

(knock on wood)

Cycling safety is definitely something to think about.

However, I also feel that one should think about the safety of other road users when choosing one's transport method.

Your first reference notes that "over half of the deaths in car crashes were to road users other than the drivers themselves". Looking at Fig 1., fatal cycling accidents that didn't involve cars were almost all (~92%) fatal to the cyclist rather than to other road users.

EDIT: And then there's the contribution to air pollution-related deaths to think about as well, see e.g. https://www.independent.co.uk/news/uk/home-news/nearly-9-500... (2015), and I guess more broadly the contribution to climate-change related fatalities. I appreciate these are difficult to measure.