This is certainly not a new idea. In addition to oil immersion, there was also deionized water immersion as well.
Potential problems with immersion set ups should be obvious. Leaks, separating equipment to be immersed vs not immersed, desk/floor space, cost.
Regardless of the cooling system you choose for your PC, the physics remain. You are removing heat from one medium and transferring it to another, and perhaps across several mediums, but in all cases, the end medium is always air.
Air coolers are the obvious base set up. A heatsink to gather the heat from the chip and transfer it to the air by dissipating it over large surface area of the fins. A fan helps speed that process.
Water coolers work no differently. They use water to carry heat from the chip into a radiator where fans blow through to speed transfer of heat to the air. Water cooling provides advantages with space constraints as the radiator can be external and as as large as you want. Air coolers are limited to the size of the heatsink you can mount in the case. Water cooling also makes it easier to add cooling blocks to things like video cards, RAM and even hard drives if so inclined.
It is this reason I don't understand this "new thing" about self-contained water loops with tiny radiators with a single fan on them. In some cases these little radiators are smaller than the heatsink of a good air cooler. In fact, if you look at the performance of many of these small water units, they are actually worse than most of the good air coolers and it isn't surprising. That's not to say they are bad, they just aren't as good.
To make a water loop that's effective you need to take advantage of the ability to have your radiator outside the case with no space constraints. The "idea" behind water cooling is to use waters faster heat dissipation abilities to get the heat off the chip, then move it somewhere you can dissipate it quicker to the air. The more radiator you have, the more heat you can dissipate because as mentioned, in the end you are always dissipating your heat to the air, so the bigger your heatsink, the more you can dissipate efficiently.
Of course, noise is always a factor. Note the fans and speeds that many of the small closed water loop units have. 120mm fans spinning in excess of 2000-2200RPM. They're noisy, but they have to be. They're attempting to dissipate the same heat through what amounts to a smaller heatsink, so the trade off is more air, which in turn means a faster turning fan. At that point, why spend the extra money, have the associated potential risks and just put a faster spinning fan on a good air cooler?
When you think of water cooling, think big radiator(s) with slower turning, larger fans. That way you gain better cooling capacity and low noise. There really is no substitute for heatsink/radiator surface area as you always end up dissipating to air in the end....unless you can stand the noise of high speed, high CFM fans.
The downside to water cooling is space to mount the radiators and fans somewhere on or near the PC and the associated issues with pumping water through and around electrical equipment/parts. I personally only advocate water cooling for someone doing extreme overclocking who needs the ability to dissipate higher amounts of heat, and even for modern chips, there are a few air coolers that do very well even with moderately overclocked systems. Water loops are expensive, especially proper ones. Some folks incorrectly believe they need a water cooler when all they really need is better case flow (remember, an air cooler is dissipating the heat from the CPU inside the case, so good case flow is needed to get the heat out and cool air in).
Oil/water immersion provides the ability to cool the entire motherboard, meaning chipset, cpu, video, ram, etc (all the parts that can go in the medium), but in the end, the result is the same...you still have to dissipate the heat and you will do it to air. That immersed system will need a pump and radiators and so you are back in the same boat. You may, may not have to make accommodations to cool the parts that can't get immersed, like mechanical hard drives, optical drives, etc. The complexities around immersion are even greater than water loops and likely more costly with little to no added benefit.
We can go beyond water and immersion and look at phase change and peltier based cooling as well. Phase change is basically a refrigerated cold plate. It uses a compressor and coolant exactly in the same way your refrigerator does. There is no doubt these systems will perform better than air, water or immersion, but at an extreme cost, both in terms of money and complexity. Condensation is always an issue with phase change and are noisy, both the fans and compressor (remember, they still use a radiator and fans to dissipate to air). They are also very expensive.
Peltier chips came onto the scene for a while and all sorts of contraptions were created around them, but ultimately they are very inefficient, difficult to work with, expensive and the issues with them just aren't worth it. If you don't know what a peltier is, it's basically a chip/wafer device that uses electricity to "pump" the heat from one side of the chip to the other. The idea is that the cold side gets really cold, and it does...but...to make a Peltier work requires a separate power supply to power the chip and they use huge amounts of energy, lots of amps. That energy put into it emerges as heat on the hot side, so in addition to dissipating the heat from the device to be cooled, you now also have to take account the added heat from the power put into the Peltier to run it...and I mean we're talking a LOT of extra energy which means a lot of extra heat. Your heatsink/radiator/fan set up would be massive...way more than for making a good water loop. Since the cold side of the Peltier goes below ambient, you also have condensation issues, just like with phase change.
It is possible to size your Peltier and it's cooling range to stay just above dew points of ambient to avoid condensation, but that means tedious temp/humidity measurements that can vary quite a bit day-to-day. It's also possible to water cool the hot side of the peltier, but peltiers work best when the hot side is...well...hot. The "operating range" recommendations for the hot side on most peltiers is well above the boiling point of water anyway.
So, to sum it up:
Air cooling is the best solution in terms of performance and cost for probably 95%-98% of all PC owners, especially with the coolers available today.
Water loops are a viable set up for extreme overclockers and provides the ability to cool other parts of the system that may need it in that overclocked environment, like RAM or chipsets. I would still recommend a very good air cooler for moderate overclockers. If you aren't pushing your CPU to very high limits, but still have heat issues, chances are it's your case flow. Water is an expensive fix that's not necessary in that scenario and may mask heat issues with other components of the system.
Immersion is strictly for the tinkerer and the "wow" factor. There is nothing you can do with immersion you can't do with air or water loops that will make much, if any difference in the end.
Phase change is for someone looking to go really extreme and also has the wallet to afford it (not to mention the ability to withstand the noise).
Peltiers are extremely niche. I say that only because there are still folks out there using them and trying to reinvent the wheel, and in most cases discovering what those before them discovered; peltiers are expensive, energy hungry and ultimately more trouble than any benefits they provide.