Perhaps, just perhaps your car is to blame here

you have no CarPlay, and you have no blue tooth. I’m sorry but how are you expecting to have it work handfree with you vehicle? Sound like you need to get a better car.
On our Mercedes GLC43 I hold down the voice command button on the steeringwheel slightly longer than a single press and it bypasses Mercedes linguatronic ans instead activated Siri over the speakers. That is standard behaviour via the wireless protocols. And you can talk normally to her.
It's just an older car, like a pretty big percent of the population. Again, if hands-free is supposedly about safety, then wouldn't we want hands-free operation for what must be the majority of drivers, too (not just the CarPlay minority)?
I have the buttons, but they aren't connected to anything since I don't have those options on my particular model. But... as above, neither do a lot of drivers/cars.
I guess I expect it to work like common sense tells me it should. "Hey, Siri... who's calling?" "Hey Siri, send call to voicemail." "Hey Siri, answer call on speaker." Hey Siri, hang up."
I also don't get why it can't route audio properly, like playing a phone call audio over the car speakers, just like it does music, podcasts, and directions.
Mine works well in my Acura. I use the buttons on my steering wheel to invoke Siri, answer and hang up calls.
Yeah, as noted above, my buttons don't control it because I don't have those options on my model of car. What about people who don't have these buttons? They either have to pull over (or, more likely, many of them look at the phone and reach for it, which is dangerous with a modern smart phone... we used to be able to just flip open our dumb flip-phone years ago, which was relatively safe in comparison).
CarPlay is designed specifically for it not be distracting. The driver should never be distracted by things having nothing to do with the car’s performance and the traffic ahead.
Split screens and pop-up notifications are the biggest distractions and cause accidents.
Well, studies have shown just having a screen in a car is already a distraction... EVEN IF IT IS OFF! But, modern touch-screen cars are a big problem.
What I think people are complaining about, though, is that for example... if you're using Waze, etc. and invoke Siri, it shouldn't blank out the whole screen with a Siri screen or things like that. With a bit better thought and implementation, it would be smarter about how it displays things when in CarPlay mode (or some kind of driving mode). The OS can obviously multitask, it is the display logic that sucks.
But, I agree about split-screens and such. As I mentioned above, the screen in general is a problem when it comes to distraction and causing accidents. But, it's a bit better than fiddling with a phone sitting in the center console, I suppose.
My point, though, if designed correctly and Siri actually worked, there wouldn't be a big need for CarPlay in the first place. But, it would sure be nice if drivers had a few specks of common sense, which seem lost on most people these days.