Rain does not make in-city cycling significantly more dangerous, and is definitely fine for inexperienced cyclists. But if people cycle regularly, they aren't inexperienced, anyway.
In areas with frequent rain, people are practiced in carrying waterproof overclothes and such. Sub-zero temperatures, snow and ice can be a much bigger problem, of course, but good maintenance resolves a lot of that, too, as it does for cars.
As noted by drakonka, you continue to argue the infeasibility of something that works well for many cities/countries, citing things that those with experience know aren't a big problem. Sure, you can't just suddenly start cycling when your life/city is built around driving tens of miles, but a city/country can work towards biking in a way that has worked well around the world.
Sudden braking from a fast speed might be more likely to cause a skid (same as a car but scaled down), but if you're popping down to the shops or commuting to work, you likely will be cycling in a more relaxed style anyway. If you're uncomfertable with braking in the rain, I recommend finding a quiet strip on a rainy day and seeing what it's like. Actively try to skid so that you know what your bike's limits are - from decade of experience cycle commuting in a famously rainy city with some highly aggressive drivers, I've never found the rain to cause additional issues beyond getting wet if I'm unprepared.
The only time I have ever come off my bike by my own fault was skidding over a patch of ice about 9 years ago, so I would recommend higher levels of caution in the snow.
When you get a bad feeling about something, it's often an indication of implicit knowledge that you might not be consciously aware of. In this case, I'd suggest your brakes might need maintenance/replacement. As the sibling post here notes, you shouldn't be working near the limit of your brakes in normal use, anyway, and so a small reduction in their ability in rain shouldn't be a problem.
In areas with frequent rain, people are practiced in carrying waterproof overclothes and such. Sub-zero temperatures, snow and ice can be a much bigger problem, of course, but good maintenance resolves a lot of that, too, as it does for cars.
As noted by drakonka, you continue to argue the infeasibility of something that works well for many cities/countries, citing things that those with experience know aren't a big problem. Sure, you can't just suddenly start cycling when your life/city is built around driving tens of miles, but a city/country can work towards biking in a way that has worked well around the world.