I really like the Noctua cards they're collaborating on, it's not really necessary to go water-cooled once you've got a 4ish slot card/heatsink with quiet 120mm fans!
Sure, but especially in a data center that’s a huge waste of density for compute. Only a single card in the space for four. Even less, really, because that card ideally has a gap for the non-blower cooler
Water cooling is just a way to transfer the heat to a larger heatsink somewhere else. It doesn't magically absorb the heat but just adds complexity and overhead. If there's a way to make a direct heatsink work, then that's the more convenient option every time.
For datacenters it would make more sense to make it all water cooled though, since you can likely have one central loop connected to an HVAC unit or something.
Water cooling is more than that. Heatpipes have much lower transfer rates than pipes with water flowing. Pound for pound you dissipate a lot more heat with water being pumped through the rad.
Ignoring that, putting the radiator anywhere other than the precious motherboard real estate has a lot of value. It's such a waste to hang a 10 pound piece of copper over all of those fast, unused PCIe lanes.
I think there are some cases with a daughterboard containing the GPU slot in a separate “heat compartment” from the rest of the case. The PCIe is extended over to that board so everything else should still be standard. It probably adds some small latency, though.
It also removes a big chunk of metal and fans taking up space on your motherboard, covering other slots. It adds complexity, not really sure what the "overhead" here is that you're referring to.