The 4-20 ma range is a "standard" adopted by tradition and also ANSI 50.1, and most process instruments and controllers use it.
It does have several advantages:
The 4 ma "bottom of span" signal allows the receiver to detect a broken wire or failed instrument.
Since the loop current never falls to zero, the instrument can be loop powered, allowing for two-wire devices.
20 ma is low enough to be made intrinsically safe, making it easier to apply in hazardous locations.
The constant-current feature of a current loop cancels out voltage drop errors due to long wiring runs (of course this would also be true if you selected different current values for zero and span).
The 4-20 ma signal dropped across a 250 or 500 ohm resistor creates a very convenient 1-5V and 2-10V, respectively, also fairly standard ranges in the industry.