100% this, the ultimate performance of a cooling solution is how fast you can move heat into the working fluid and how fast the radiator can move it out of the working fluid.
AIOs confer no particularly special advantage in either. The fact that the working fluid is water means nothing, heatpipes actually use water internally too. The difference is that heatpipes are actually evaporating the water so they can actually more more heat energy (due to enthalpy of evaporation) than AIOs.
AIOs actually tend to be louder for a given amount of cooling due to cheaper, louder fans and crappy noisy pumps. Custom loops don't really suffer that but they also cost 10x as much. They mitigate a lot of the downsides like pump noise by throwing expensive, high quality components at it. That's fine as far as it goes, but AIOs themselves are not an automatic win.
A large air cooler (eg Noctua NH-D15) is going to perform very similarly to a 240/280mm with identical fans (Noctua) at the same RPMs/noise levels. The difference is that most AIOs ship with very cheap fans that are just designed to spin fast and be loud, but that cools quite effectively. You can punch up the fans on a big air cooler and push a lot more heat through them. They just are optimized for silent performance out of the box.
Furthermore, most situations are currently limited by the IHS. AMD once pushed 500W through a 120mm radiator on their 295x2 card (OC'd), and temps would stay under 60C while doing it. The radiator size is not as big an impact as most people expect, moving heat out of the loop is not the bottleneck, it's how fast you can move heat into the loop that matters. GPUs do that very efficiently (bare die, dual chip on the 295x2). 5 GHz 14nm chips push an incredible amount of wattage, 7nm chips are so tiny that they result in very high thermal density, making both of them fairly prone to IHS thermal limitations. Colloquially: the heat just can't move out of the die into the IHS fast enough. The surface of the IHS is actually fairly cool, the liquid inside an AIO is barely above room temperature, but the heat just is not moving into the loop very well.
There is a resulting thing where people splurge on high-end gear, say a 280mm, and see high temps and tell themselves "wow, good thing I bought a 280mm, a 120mm would have been way hotter!". And no, not really, the amount of radiator fins isn't the limitation, it's how fast you can move heat into the loop. If you put a probe inside the reservoir to actually see the temperature of the fluid, it would barely be different between a 120mm and a 280mm.
And in fact the temperatures would probably be barely different than if you bought a NH-D15, or a Scythe Fuma, or other large multi-tower cooler. At the end of the day the working fluid doesn't matter, it's all fins and airflow.