Your parents didn't even try to educate you, did they?

I have a bachelor's in civil engineering, and that's part of the reason why I'm able to pierce through the deep coating of carbrain induced status-quo thinking.

You're making all the wrong assumptions right from the start.

At a small stop-go light, like you might find in a residential neighborhood

These shouldn't even exist. A residential neighborhood shouldn't have traffic lights, and it should have a low enough speed and low enough volume of cars (only the people who live there should be driving there) that accidents should be rare and low risk.

The fact that you assume there's a traffic light here starts from the basic assumption that there is so much car traffic that it needs managing. You've already designed your residential street wrong then.

A more medium size intersection

Skipping this, because these intersections shouldn't have ANY bicycle interactions at all. If bikes are crossing your 4-lane divided highway, you've already designed your roads wrong. I would argue if you're putting a full streetlevel crossing in, you're also not doing great unless you get paid per traffic jam.

Note that these are two different environments; at an intersection in a city center, the speed limits are often 20mph, and frankly, bicycles should not have their own lanes there. By law they're vehicles, they should be in traffic behaving the same as cars and have the right of way that cars do. Where they get themselves killed is trying to weave in and out of traffic, or insisting on putting in a parallel bike lane pretending it turns off friendly fire. "Just add to every driver's cognitive load and make them responsible for my safety." Fuck off.

A protected bike path and protected intersection REDUCE everyone's mental load because it makes it practically impossible to hit a bike. And it separates bikes from traffic too, so they can't weave.

The problem with American bike gutters with painted lines is that cars enter them constantly, by design. Cars cross the bike lane to park, they cross it to turn right, and something they just drive in it because the drivers are idiots. Or cars park in it because they're idiots. And every time a car enters the bike path, the bike needs to move or die. So they move, creating more risks.

All of those problems go away with a raised barrier between the bikes and the cars. You can just stop thinking about them, because they're in an entirely different lane that you physically can't even get to. And if you turn right, you can treat them like any other vehicle again, where they'll have the right of way or there's a traffic light.

Meanwhile, back out on Some Road and Another Street, these have 45 and 55 mph speed limits, you're traveling from town to town here, and these places pretty much should not see bicycle traffic.

Depends. A 20km bike ride is totally fine, an 80km one isn't. But if there's cars going 55mph right next to me, I won't be taking a bike because that's super dangerous. There should be a seperate bike path there as well, removing all risks.

Of course, only if it's actually inhabited in that distance.