Fuel injectors require filtered gas because even small particles can clog them, and said filter is more likely to be clogged or even compromised by sucking up the last drops of fuel (and scale and debris) in the tank, so the low-fuel warning is required.

Carb jets can get clogged, too, but are wider since they're not under as much pressure. Also, since they're a wear item they're a lot easier to clean and/or replace.