Why not a 0W or 5W; because it gets increasingly difficult to have an oil that flows when cold AND!!! maintains sufficient viscosity when hot. The goals are not mutually compatible.
You will almost never find a 0W30 conventional oil, because the cold weather characteristics necessary to meet the 0W designation do not allow the oil to be a 30 weight when hot.
5W30 is possible with conventional oils, but to do so requires fairly large quantities of viscosity modifiers. These additives prevent the oil from thinning at operating temperature. They do tend to wear out and breakdown; this is where the term "shearing" comes from. The oil (really the viscosity modifiers) shears down, becoming thinner at operating temp., and this can lead to higher consumption and/or deposits.
Synthetic oil is, by its chemical composition, better at meeting the cold/hot requirements. A 10W30 synthetic may in fact be a straight weight oil that, through its chemistry, can still meet the cold temperature pumpability and cranking requirements AND! be a 30 weight at 100c. Still, large spreads like the 5W50 do require the same viscosity modifiers to perform at both ends of the temperature spectrum, and shear can be a problem with some of these synthetics as well.
What to do...use oil (especially conventional)with the narrowest spread possible; 5w30 and 10W40 can be more likely to breakdown, given the above info. 10W30, 15W40, and 20W50 tend to be more stable for longer periods of time.
Synthetics allow for much greater flexibility, but at a much higher price.