You are over generalising. I don't know where you are but where I am in western europe cyclist absolutely cross intersections like a vehicle.
The trick is to take control of the lane. If you are sticking to the side cars won't see you. If you take up space in front of them they will see you and include you in their calculations.
And before you or someone else jumps here to spread some fud: No i am not advocating jumping in front of cars with zero warning. Or whatever silly idea you have based on what I just wrote. I see this done all the time, and I do it fairly regularly.
You have to be seen. You have to be predictable. You have to know where you are heading.
But just as you don’t signal and start your left turn in your car at the last moment, so you don’t with a bike. Unfortunately, we have bikers who go to a left turn from the rightmost position, don’t signal or signal when it’s useless. The rule for drivers is to expect and anticipate stupid people and not kill them.
And the same thing on roundabouts, if you want to safely ride a roundabout you absolutely have to take the entire lane and not allow cars to overtake you. Otherwise cars exiting the roundabout will run over you.
For the record, I personally prefer crossing twice as well. But I'll disagree with "western Europe".
E: Source: https://www.stadt-zuerich.ch/pd/de/index/stadtpolizei_zueric...
For California, I don't know. For western European: Oh my god YES! By all mean signal which way you're going to turn, but in intersection, especially those with multiple lanes, you never make a left turn. Drivers will not expect you in the middle of the intersection.