Bicycling

Because you still need to yield for pedestrians.

Of course. I'm not suggesting that you blow through the stop sign while other people are there! That's not how an Idaho Stop works.

I can imagine any reasonably size truck, semi etc turning left may need to use the bike lane to avoid clipping the front of a vehicle in the lane coming through from the other way.

That's a reasonable concern. In areas where large trucks are expected to turn, you'd see traffic lights (not stop signs). At least, that's what I've noticed, since the intersections themselves need to be large enough to accommodate large trucks like that.

But three ways in areas where you'd only expect small vehicles are very common around here, and stopping doesn't make sense.

Really, we just need to permit the Idaho Stop so a question like this one becomes irrelevant. 😂

I'd ride through it if nobody is around.

I'm not taking chances that someone won't swing too wide and smash into me if there's traffic though.

Exception is oncoming traffic, because they won't be closer than 20ft to me unless they're aiming

People are dumb. Expect them to do dumb things and you'll live longer.

If a cyclist can ride right through this, why can’t I on my 125 motorcycle?

Perhaps it should be allowed! Cars already treat stop signs as yields ("California Roll" is the car corollary to the "Idaho Stop"). Why would you stop if the car behind you isn't planning to? (I'd love to see motorbike studies on this; please link me to some if you know any.)

Studies have shown that cyclists treating stop signs as yield signs leads to fewer accidents, both with cars and pedestrians.

Yielding also decreases time spent in the intersection. You have a motor underneath you. Cyclists don't. Clearing the intersection quickly prevents cross-traffic from splatting you. That's why slowing down, checking for traffic, but not stopping is so important for momentum vehicles.

The NHTSA (the US road safety org for my Canadian friends) has a good two-pager overview. It's a good place to start if you're still curious about the reasoning behind the Idaho stop.

So, respect cyclists as much as car drivers, except when it’s inconvenient for you to follow the rules of the road?

Just to put this out there: this isn't really about convenience, but safety. My question is basically "why isn't an Idaho Stop permitted at a 3-way shown in the photo?".

Since we know that Idaho Stops are SIGNIFICANTLY safer for cyclists (and yes, it can be more convenient as a secondary benefit), it's not really about respecting or following rules, but "does this rule make sense for a cyclist, when it offers no benefit to safety?".

Intersections are probably the most dangerous place on the road, or at least that’s what I was taught in motorcycling class 40 years ago.

Yes, if you are driving in the middle of the road, not in the gutter lane. And usually at 4-way intersections where vehicles cross each other's path. You get none of that in this context.

If a cyclist can ride right through this, why can’t I on my 125 motorcycle?

As above, that would be dangerous. Unless you can provide evidence that blowing through stops on a motorcycle is actually safer for you.

Are cars allowed to park in the intersection there?

Generally speaking, cars are usually not allowed to park within a certain distance of any intersection. Do they abide by those laws, designed to keep other road users safe? Of course not.

I've come across so many of these three-ways where it really doesn't make sense for cyclists to have to stop. Even more so when you are forced to stop at a light (that will never change due to no cars being around you), and simply permitting cyclists to ride through in the bike lane just seems like a no-brainer.

In that example, you're right. Not that it would make a difference, since there are crosswalks in places that permit Idaho Stops. But in other 3-ways, especially in residential areas, crosswalks are absent (so are sidewalks on the right side), so stopping feels... off.

Take this example:

Ignore that the bike lane "'continues" through the stop, as this stop sign is pretty new and the lines were already painted.

There's no sidewalk on the right side, and no crosswalk at those stops (only on the left side). This particular area is part of our waterfront trail, an extremely popular bike route. It would make sense for cars to stop there (they speed down this road on a regular basis), but bikes?

There still being a crosswalk there is a reasonable excuse

Do they not have crosswalks in States that permit Idaho Stops? How are those intersections managed (all of them, really)?

Cars are the danger at any stop, not bikes in the very far right of the road. But yes, if pedestrians are crossing, everyone should be stopping.

The less complex the traffic rules are the easier they are to build signage for, learn, and follow. Everyone stops at the stop sign. Plain. Simple. Easy. Safer.

That would be nice, except that motorists aren't following those simple rules, and they are the ones running people over. When cyclists follow rules designed for large vehicles, it actually doesn't make them safer.

This is why having the same rules for "everyone" doesn't work. Everyone should understand the responsibilities of other road users (including when pedestrians should be given the right of way and what that looks like), but not everyone should have the same rules if it doesn't make sense or puts them at greater risk.