1-When you analysis the circuit with Short Circuit Conditions, Y-Parameters are useful.
2-Balun Circuits can be driven ODD Mode or EVEN Mode e.g. Driving Currents/Voltages may be In-Phase ( Even Mode) or Out-of-Phase (Odd Mode) ( like Parallel Coupled Transmission Lines ) therefore there are 2 Characteristic Impedances.ODD Mode and EVEN Mode, so there should be 2 set of Reflection Coefficient/Transmission Parameters/S-Parameters.