Is 240V to 24V DC PSU to 120V 60Hz inverter a low cost way to convert 240V 50Hz to 120V 60Hz?
What you say will work, but will be inefficient and not "cheap" at those power levels.

24 V is not a great choice of intermediate DC voltage since the current will need to be quite high.  Do the math.  (2 kW)/(24 V) = 83 A, and that's not even accounting for the inefficiency of the inverter.  Higher voltages allow for lower current, which should help with both price and peformance.