I understand that lower viscosity oils are way easier to pump and move around engine parts, also they form a thinner "film" on friction surfaces which could improve parts measurements precision etc. Is it only due to increased piston rings leakage that we don't use extremely thin oils? Are they more prone to failure in operating and high temperatures? Are these oils easier contaminated? Maybe they are very expensive to produce???
Thin oils tend to have a very poor shear stability, especially when they are hot. The function of the oil is to protect and lubricate the engine and ancillaries (i.e. turbo chargers). In certain applications it also makes up some (where an oil cooler is employed) or all (for aircooled engines such as the Beetle) of the circulated liquid cooling system.
I'm not sure that an oil which is consistently thin and remains so once upto operating temperature exists. Most engine oils are chosen so that they will provide some protection at cold start but optimum protection when they reach their target temperature.
Tribology is a huge topic...
But, the thinner the oil, then the more oil in terms of volume and/or the higher pressure is needed for a given tolerance between bearing and surface.
So many things are taken into account when specifying the oil for a particular use. Operating temperature, load on the bearings, relative speed of the bearing etc etc
We are, or are starting to, for exactly the reasons you quote.
New vehicles (VAG group for example) are starting to use 0W20 oil, with 0W16-capable engines coming soon and tests being conducted with oil as thin as 0W8.
Source: MTZ worldwide 12/2018, "Potentials and Risks of Reducing Friction with Future Ultra-low-viscosity Engine Oils"
So the main reason of using oils in lubrication is to separate the surfaces from contacting by a "thin film" of oil. All the other reasons are of course also there, but for now let's assume everything else is under control. Now the thickness of the oil directly depends on the oil viscosity - thicker oil means thicker film. In the past, when the materials were not so good, engineers tried to use "thick" films in order to completely separate surfaces. Thus the oils were highly viscous. But of course, high viscosity of the oil also generates high friction, meaning losses. So thats why nowadays there is a trend in going to thinner oils. It is now possible since the theory behind the lubrication is very well developed, materials and design of elements got much better. I hope this also helps. Here is a link to the description of the theory with a simple online tool that shows you how the film depends on viscosity of the oil.