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Assumptions:
So why do those bikes use thin tires, and not 2" slicks?
I think there are a couple of flaws in your knowledge that help determine the prevalence of skinny tires.
Firstly, narrow tires exhibit significantly less rolling resistance than larger volume tires. This has benefits and drawbacks, with the benefits being easier commuting due to less friction. The drawback is that there is a smaller contact patch with the ground and hence less grip, but on smooth paved roads, asphalt etc. this is not a large problem. Also, slick tires increase the grip due to more rubber contact and less grooves between knobs compared to a similar volume and diameter knobby tire.
Aerodynamics is not a huge factor in the equation, as you pointed out, since low speeds around 20km/h are only marginally effected by air.
On the issue of air pressure, I think the pressure-for-pressure comparison between skinny tires and larger volume tires is a bit of a misleading statistic. Skinny tires run exceedingly high pressures - racers are all known to use upwards of 80psi and as high as 120psi! Compare this to a larger volume tire, like that on a mountain bike, and pressures of around 30psi are about the norm. MTB tires like this are often rated for much higher pressures than they will ever need, but many will take use of this in order to use a MTB tire on the road, for example (I often run 50psi on 2.1" MTB tires for more efficiency on the road). Pressure ratings on tires simply refers to the uppermost limit of safe use before there develops a significant risk of tire blowouts or some other failure. However, the relationship between rolling resistance and tyre pressure is completely different for road or MTB use. On a MTB, lower pressures offer lower resistance due to their ability to deform and mould to the terrain, essentially flattening out the ground. This effect is useless on a paved road, where the surface is almost completely smooth. So on a road bike, or a city bike, higher tire pressures will correspond to a lower rolling resistance, and thus a smaller volume tire would be preferable.
One thing to note is that tire pressure makes little difference to rolling resistance at high pressures (until the pressure is low enough for the tire to be deemed flat, which is always bad). Consequently, a skinny tire will have to be pumped up less often. Factors that make more of a difference to rolling resistance are the compounds used in tire construction, tire shape and tread patterns.
Finally, in my experience, punctures are not any more likely to occur on a small volume tire. If anything, they would occur less due to the decreased footprint/contact patch. The main cause of punctures are surface conditions, such as glass shards, sharp rocks, nails and other debris. These objects are equally likely to be found on any given bike, but easier to avoid with a skinnier tyre, because the gaps between hazards are relatively larger compared to the contact patch. I believe the reason for this assumption is that high pressure tires can have much more audible and noticeable punctures, and the escaping air will do more damage to the damaged tire when pumped to 120psi than 30psi. The puncture itself is no more likely to occur in the first place.
In conclusion, city bikes that are optimised for paved, sealed roads are prime candidates to use skinny, almost race like tires and consequently reap the benefits they offer, as their daily use will almost never take the bikes outside of the optimum conditions for such a tire.
Old comfort bikes with rim brakes had narrow(ish) tyres because that was all you could fit under the brake calliper with a mudguard. Cheap rim brakes that work well and are compatible wide tyres (ie modern V-brakes) are a relatively new invention. Tradition and aesthetics are probably the main reasons why some manufacturers continue to fit their comfort bikes with unnecessary narrow tyres.
Traditional Dutch bikes were build to take 32 mm tyres, maybe 35 as maximum.
All parts were designed on that size of tyre, as that was what was available. (I am talking about 70 to 20 years ago, maybe even shorter time ago.) That is what the Dutch are familiar with, that is what they are used to, that is what they know that works and they do not see reasons to change that.
If the Dutch want wider tyres, they go for a bike which is designed for wider tyres, mountain bikes for example. Not for a traditional Dutch bike.
With the new ranges of Electric bikes you see a bit more variation, but still most bikes with traditional frames go with the traditional tyre sizes.
As a user of bikes with traditional tyre sizes, 32 mm most likely, I have never seen the need to go for wider tyres. This is what I am used to and this is what my bikes (and trikes) are build for.
I see tens of bikes each day in my morning and (late) afternoon commutes and many more on days I do a bike ride in our nature area near here, and very few of the bikes you see do have much wider tyres. (There are some, certainly, but it is a small percentage. Those that are not mountainbikes are very rare.) This is all paved roads and mostly either tarmac or well laid bricks, and on a sit up bike you do not need shock absorption. (On my recumbents I want some help to absorb the shocks, as I am not able to get up when going over the railway tracks.)
You say that thin tyres run punctures more often and need pumping up often. I use a trike at the moment, with 3 20" wheels, all three are not protected against punctures and I have had one slow leak in three years. Normally I pump once every 6 months or so, not often enough to worry. Now I am at the time they need replacement and I rode through glass recently, I now pump once a month.
The same rate of punctures and pumping has been common for me. And these are bikes that are used daily, 10 km per day these years, with the odd 50 km ride in the weekends.
All above is for the Dutch, on Dutch roads and with the Dutch traditions. But that is the style of bike you talk about. Your experience in other parts of the world may be different, but you may need to tell your city that the roads need resurfacing.
I wonder if you think about road racing bike tyres, which are narrower, need more pumping and are designed for much higher pressures.
Pavement requires less shock absorption and less grip.
