Tagging along potentially doubles the capacity of the intersection. Since it’s blocked by one person coming through in your direction, you are not adding any burden by going through - and you are adding burden by not going through. In microeconomics we had a word for this. Pareto-optimal? You’re obligated by self-interest to act when something you can do (a) helps at least one person, and (b) harms nobody.
I’m pro tag along, but no one has addressed question #4
Here in California, at least, if you go through the intersection before the pedestrian has passed, you will get a well deserved ticket.
You may have the right of weight, but the ped has the legal right of way.
WhereI used to live there was four way stop just down the street. The east-west were three lane(left turn, straight turn, right turn). The north south-street was only straight, and right turn(There is always a right turn lane in Colorado, even if there isn’t one 
). Plus it was offset by about 25 feet so straight involved a right turn, and left turn anyway. It was a pretty busy place, and there were a fair number of peds too. Fortunately it was of no use to non-locals, so 99% of intersection users knew exactly what they were doing. Some days I would just watch, as it was an amazing ballet of turns, swoops and slaloms, going through efficient as hell. If everybody had done it legally it would have taken three times as long, but going through at least a thousand times I never saw a near accident, or heard a horn honk.
It’s my understanding that everyone at a 4 way stop is an idiot and doesn’t know what they’re doing. I’m very impatient with these people and have serious road rage issues anyway, so I tend to cut in line a whole heckuva lot at 4 way stops. If I pull up the stop sign and no one moves in about 3 seconds, its my turn regardless of who was there first.
There should be no hesitation at a 4 way stop. You should know your turn and take it immediately when you’re up. If you don’t, I’m not going to wave you through. I’m going to go.
I really can’t see any reason not to. If one car is exercizing its right-of-way, there’s no danger in another vehicle making the same maneuver right next to it.
As for traffic circles, we have one (1) in San Francisco, between Taraval/Portola/Laguna Honda. They tried putting a few in on Page St, but that was annoying more than anything else.
Our town loves 4-way stops. (And 3-way stops in a 4-way intersection, but that’s a rant for another day.)
But we don’t have any that are like the one in the OP. If there are multiple lanes at a stop-sign, one is for turning left and one is for going straight or right. Both of those people can go at once. And also multiple right turns can happen at the same time.
People don’t know the rules. It’s strictly first come, first served, and ties go to the person who waves them through. It gets so bad sometimes that I’ll slow down a bit, so I don’t hit the stop at the same time as someone else, which means there’s no waving involved.
/slight hijack/
Jeez-Dang I hate it when people try to waive their right-of-way.
Yeah… they’re being “polite”, but there’s way too many variables at work.
Cars turning, cars going straight, pedestrians, keeping an eye on the kid with the bouncy-ball in the corner yard to make sure he’s not gonna dart out in front of you, etc.
No thanks… please take your lawful place in the right-of-way sequence.
Besides, you’re fifty-plus feet away, behind angled glass windows and windshield that’s reflecting sunlight or streetlamps and I’m trying to pay attention to all of those variables.
Oh yeah… and DON’T get pissy with me if I don’t see your little half-wave directing me to precede you with you mouthing the words “Go on.”
Follow the rules and we’re all better off.
Thanks for allowing me that.
/here endeth the slight hijack/
Yes, I tag along, and I get annoyed when some fool in front of me doesn’t.
if someone else tags: good move
when I tag: even better move!
when someone waives their turn: asshole!