Inequality is not necessarily bad, there is "bad" inequality and "good" inequality from an economic perspective.
If we talk about absolute equality, Marx argued that communism may need to start with despotism (which tends to be very unequal). He mentioned that at first we will need to have an authoritarian government to force everyone to accept the system, which can then, perhaps much later on, be converted into a communist democracy... once everyone is used to the new economic reality. China made that same economic statement at the beginning of their great economic revolution, that first they will develop the economic centers, creating inequality, and then it would spread through the rest of the country.
These strategies are very dangerous since there is no guarantee that wealth will trickle down and definitely no guarantee that the new economic elite will gladly let their power decrease for the benefit of others... Inequality of opportunities of whatever type is bad for society, including the economy.
The chance to get better living standards, which could be having more stuff or having better working conditions or having more free time (or whatever makes you happy) leads people to try harder and to get more skills. As such, economic inequality (based on equality of opportunities) tend to increase productivity, which in turn improves the economy (again, not just in the amount of stuff we can buy, but our living conditions in general such as health for example). The problem with inequality of opportunity is that a good amount of people with low opportunities can have high productivity... and a lot of those with good economic opportunities (you rich kids from Lima) have very low productivity...
If you want to talk about inequality between countries, then I agree we need some countries to produce more agricultural products than others (because they happen to be situated where there are good conditions for that) while others should produce more energy (because they happen to have good conditions) while others should produce more technologies (again, because their culture is better suited for that)...
However, while we cannot all be rich (we need several planets to be able to do that... and we only have one) we can all be good and comfortable. The current living standards of the rich world is impossible to maintain and spread over all of humanity (unless some fundamental change happens) but something quite acceptable is possible to attain.
As for innovation, it is a misconception that important innovations need to come from rick countries. We've had some very important innovation coming from Africa (cellphone related technologies) and from China (Thorium nuclear energy for example) in the past few years. We may not develop I-pads and I-phones and cars that can run faster than 300 km per hour but we would still have productive, useful, and most importantly relevant innovations. As such, agricultural countries can also become highly innovative places.
I must say that the political will or even feasibility of a "balanced" world seem unreachable to us indeed. However, it is technically possible to have an economic order in which we don't have poor (on a relative scale of course). In such a system, "good and comfortable" would be the best we can obtain. That said, we would still need economic inequality based on equality of opportunities to get the best out of our scarce inputs.