1. As Valantar said: silence is much easier achieved with water.
What exactly? Heat radiation, silence or etc?
2. If you use your AIO's radiator as exhaust, then absolutely no heat from the CPU gets trapped inside your chassis, leading to the rest of your system being cooler.
That actually depends. In ideal conditions, a good case mostly needs cool air intake and exhaust isn't as important. The main purpose of fans is to transport cold air to hot components and create airflow, not air blow. And it's better to exceed internal component fan flow with intake fans, so that coolers aren't starved of cold air. In such set up you can be fine with minimal exhaust fans or none at all, but if you add radiator as exhaust, you block that path of flow with very air flow resistant radiator and as result now you really need more fans on exhaust, which are usually not ideal for maximum airflow. You may not heat up your case components as much by blowing hot air on them, but you create a blockage of airflow and you solve it with more fans. To create exactly the same air flow, now you need more fans and therefore more noise, potentially not so great airflow too. So I'm not too sure if radiator on exhaust is a good idea. Despite not being intuitive, mounting radiator as intake probably means better thermals.
CPU heatsinks usually aren't nearly as airflow restrictive, so they are less problematic.
3. If you have a custom loop, the combined heat of all water-cooled components gets evenly distributed across all your radiators, eliminating hot spots and transferred heat inside your chassis.
Not really. Things like SSDs, VRMs, chipsets, are still left uncooled, so they remain like they were. Despite seemingly obvious need for VRM cooler, I still don't see almost any VRM water block and that's pretty scary considering that some people decide to reduce fan amount after water cooling their rig.
4. If you want silence with air, you need a big chunky CPU heatsink that puts quite a big pressure on the motherboard. The pump / head unit of an AIO, or a CPU block has practically no weight compared to that.
AIO still has big radiator, just that you can relocate it further from chip. That doesn't change the fact that it's also big and heavy. And motherboard stress concerns don't make sense anymore as in the past boards survived really huge coolers like Scythe Susanoo, Scythe GodHand, Thermalright True Copper. Both that are heavy and have tons of torque due to how far their furthest parts are. And today we have custom CPU backplates, so weight really isn't a problem and since board is made from plastic, it's hard to break it, so I doubt that actual lack of custom backplates was ever a problem. The bigger problem is that some motherboard traces after many heat cycles may get damaged, but then again CPU backplate helps by distributing weight to more motherboard surface.
5. You're right, air coolers have come a long way in the last decade or so, but so has water cooling. The best air cooling solutions will never be as efficient as a custom loop, or the largest AIO radiator.
I'm not entirely sure about that. AIOs can be beaten rather easily, because their pumps are tiny and generally are not great at moving water fast. Custom loops can still fight, but that's mostly due to virtually unlimited reservoir capacity. You can connect anything. You can also use big radiators from cars or trucks if you fancy. You have such freedom, but if you want to build something reasonably sized, then difference isn't that big, it mostly comes down to pump. Most water coolers have less area from where they could dissipate heat, than many air coolers, so in theory, once water is saturated by heat, water cooling should be as effective as air cooling.
6. Water takes much longer to equalise, so you won't reach peak temperature in shorter workloads.
Depends on pump speed, but yes that's mostly true. Unless you have big aluminum air cooler, for some reason they are also slow to equalize.
Just a few of my reasons why I haven't had a gaming PC without water cooling (for prolonged use) ever since I touched my first AIO.
That's cool, but I prefer pedestrian air cooling and often cooler chips. Dealing with heat is a pain. As long as I can achieve decent cooling at almost no noise and low price, it's fine. That purpose is perfectly served by 120mm air coolers. Both towers and downdrafts. Depending on CPU even 92mm tower can be a big overkill.