Why do T intersections have two pedestrian crossings and not three?

Normalize Pedestrian Scrambles!

I can only offer a perspective from my area. In California, every intersection by default creates "unmarked crosswalks" in the parallel and perpendicular directions, except when prohibited by posted signage. This makes it legal for pedestrians to cross in any direction at an intersection, so long as it's not diagonal and isn't prohibited.

With that being the default rule, municipalities will either paint the crosswalk -- becoming a "marked crosswalk" -- to promote its use (even though paint doesn't prevent collisions) or will close the crosswalk outright, to steer pedestrians toward other crossing options. The latter is where things get truly messed up.

Rather than proactively mitigating the dangers to pedestrians, lazy municipalities expect pedestrians to ignore common sense and walk 400 m (1/4 mile) or more out of their way, to find a "safe" crossing at a marked (painted) crosswalk elsewhere. Outside of the downtown core, I've never seen concrete barrier-enforced crosswalks to stop wayward motorists.

Also, where freeway on-ramps and off-ramps meet city streets, these are considered intersections too, but out of sheer laziness, some municipalities close the entire sidewalk on that side of the block. So just in case an interchange area wasn't enough of a hellscape, people on foot are funneled like cattle to the slaughter.

Finally, some good (ish?) developments. Partially in response to public demand, but not actually giving full effort, some municipalities have started to add signs to unmarked crosswalks, at places where pedestrians aren't prohibited from crossing and they actively do. But these signs aren't to encourage more pedestrians, but a reminder/beg to motorists to respect the default law on unmarked crosswalks, where pedestrians have first priority.

Do motorists even recognize these neon yellow/green signs? I've not seen evidence of it. And so once again, it's all theatre, to make it look like lazy municipalities are doing something when they're not. Same as with "driver awareness campaigns" and equivalent rubbish.

So yeah, that's my spiel on bad crosswalk designs: it's always been a public subsidy towards car welfare.

Are they stupid?

If it doesn't have traffic lights:

Crossing the stem is safer, as cars need to slow down and often stop to make the turn, and reducing the crossing of the straight road to only one helps concentrate the required attention to that one crosswalk - a driver can't miss someone crossing the other crosswalk if it doesn't exist.

If it has traffic lights:

Yes.

probably based on traffic patterns and volume, perhaps visibility plays a role too.

both are reason why the one in front of our office here does not have two crosswalks across the through street. people still do cross on the unmarked side all the time.. but they're idiots that don't realize some traffic can't see them until it's 'too late'.. they get hit or the car that has to stop suddenly sits awkwardly in the middle of the intersection and becomes a target itself.

stupid is thinking a crosswalk prevents you from getting hit by a car :/