2. Soot Detergent - Soot will always be produced by the engine as a by-product of internal combustion so it is important that the oil continually be able to do its job of removing it. By design, engine oil is blended with additives and detergents to help remove soot build-up that would otherwise cling to parts and oil passageways.
3. Soot Suspension - Removing dirt and soot is one thing. The motor oil must also carry the displaced dirt to the oil filter to trap them.
4. Coolant - Yes, motor oil complements the primary cooling system of your engine. The primary cooling system typically just cools the cylinder walls and head. The engine oil cools the other important parts where coolant water wouldn't and shouldn't be. For example, most cars nowadays would have oil jets underneath the pistons to help cool them. This is besides the fact that the lubrication properties itself prevents friction and heat build-up or at least, the oil flow helps dissipate heat build-up.
All four properties are interconnected and a failure in one property can cause a domino effect. For instance, the detergent properties of motor oil will eventually deteriorate and get used up in time. When that happens, soot can start to accumulate, and if it becomes very bad, it can start blocking off passageways and tiny orifices. Afterwhich, the suspension capabilities of the oil is compromised and lubrication and cooling to certain parts of the engine can get affected.
So, waiting for the oil to get sticky before replacing them is already probably too late. Manufacturers are building ever more sophisticated engines that have very tight tolerances between moving parts. Not to mention that motor oil is also used in variable-valve technology like VVT-i, VTEC, etc. to control the cam positions and such. Consider that oil passages in these systems are measured in millimeters.
To put things into perspective, here's an example of how small an oil passageway can be... the oil control orifice on a Honda engine.
So as you can see, using old, overdue, and sticky oil will not be ideal and may in fact cause serious engine problems in the long run.