What is a flight leg and why it is so important for an aircraft?
I don't think flight leg is important for either aircraft no airline.

The reasons why most flights have one or two legs is purely economic. Aircraft have to be operated with rather high load factor to be profitable. If you have a line with less passengers, you really want to use smaller plane or run it less often. Because different links have different demand, it's rather rare to have many consecutive links with similar demand so it would make sense to fly them with one plane as multi-leg flight. And few people would want to fly the whole trip as the stop-overs take rather long.

For aircraft what matters is not legs, but cycles, meaning pressurization cycles. For pressurized aircraft the material fatigue is most closely related to the cycles and since each cycle also involves one period of running the engines at high thrust, the engine wear is also somewhat related. It does not matter whether the aircraft accumulates 4 cycles in 4-leg journey or 4 separate journeys.