I'm guessing that if you bought a 2002 (congrats, btw; I was looking into the various flavors thinking of picking one up myself, but the old-school safety standards vs modern vehicles have me very reluctant to get anything older than a ~2012MY), you didn't give BMW much / any money.
bmw got their money way back in 1975 and it certainly didn't come from me.
It is strange to own a car that is older than I am and safety is a big part of it. I have some self imposed rules that don't get rid of the risk, but do reduce it. I won't let kids ride in the car, but adults are free to make up their own mind. I only drive it in good weather and I'm pretty obsessed about maintenance. It's also tiny, so I can give myself tons of room around other cars. Modern cars are bloated (though it's annoying to be in front of pickups since the headlights are higher than my roof)
Compared to my 2016 daily driver it would much more dangerous to actually crash, but I am convinced I am far less likely to actually have an accident. The visibility in modern cars is awful as a direct result of the thick pillars required for them to be safe. In the 2002 I can see everything; there is no blind spot for cars to hide in. It also requires huge amounts of concentration to drive. The power band (what little there is) is all up top, so you have to be in the correct gear at all times. My 2002 requires actual driving, so I'm engaged at all times. I sometimes scare myself with how little I can pay attention in my daily.
If you want the same experience in a modern car get a fiat 500 abarth. Buzzy little engine you can thrash and corners on rails.
You are right about being less likely to crash. Hagerty has stats on this. It’s for exactly the reasons you state. I daily drive a ‘67 (though not a BMW) and it’s only when not foggy / rainy, I give myself plenty of room around other drivers, I avoid left turns when I can, etc.
I work from home. Drive very little. I have a barebones wrangler with no power locks, no power windows. No airplay. No backup camera. The only amenity is AC. Is it the safest vehicle? No. But it's an old body on frame, and because of that I tend to drive slow anyway. I'm a little jealous of your 2002.
BMW is dead, long live BMWs?