Why do we have to check that the fuel x feed is properly functioning before departing for an ETOPS flight on the A320?
The main reason to check the Fuel-X-FEED on the ground before the flight is to allow the pilots to use the total fuel quantity on both wings in case of a single-engine failure during flying in ETOPS.
(Due to engine-out scenario you may not be able to feed one engine by both fuel tanks without the FUEL-X-FEED Valve)

in addition to this, the Fuel-X-FEED in the A320 MEL is a NO DISPATCH item by means you can't depart without and that reason tracks back to the EASA Requirments listed in AMC-20 AMENDMENT  - 7 (APPENDIX 4 - FLIGHT PREPARATION AND IN-FLIGHT PROCEDURES):

(11)  Fuel  system
(i)    The aeroplane fuel system should provide fuel pressure and flow to the engine(s) in accordance  with  CS  25.951  and  25.955  for  any  fuel  pump  power  supply  failure  condition not shown to be extremely improbable.
(ii)   The fuel necessary to complete the ETOPS mission or during a diversion should be available  to  the  operating  engine(s)  under  any  failure  condition,  other  then  fuel  boost pump failures, not shown to be extremely improbable2 (e.g. crossfeed valve failures, automatic fuel management system failures).