B737 PLTS RECEIVED A SHORT TURN ONTO FINAL INTO LGA THAT RESULTED IN A MISSED APCH AND LATER DURING TOUCHDOWN AND ROLLOUT WERE GIVEN A SERIES OF INSTRUCTIONS WHEN THEY WERE TOO BUSY TO ANSWER.

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AFTER HOLDING FOR ALMOST 1 HR ON THE ARR; WE WERE VECTORED AT 180 KIAS ON VERY LONG VECTORS IN LIGHT TO MODERATE TURB IN THE CLOUDS FOR THE RWY 4 ILS. WX WAS 300 FT OVCST AND 3/4 MI VISIBILITY AND SURFACE WINDS APPROX 060 DEGS/12 KTS. WINDS ALOFT FROM 6000 FT DOWN TO APPROX 1000 FT WERE FROM APPROX 250 DEGS/47 KTS. THE APCH CTLR GAVE US A VERY SHORT TURN-ON AND WE WERE IMMEDIATELY ABOVE THE GS WITH A 50 KT GS INCREASE AND (CONSTANT MODERATE TURB); AND 'CLRED FOR THE APCH.' WE ATTEMPTED TO MAKE IT WORK; BUT THE APCH BECAME UNSTABILIZED. COMMENCED GAR AT APPROX 1200 FT. WE WERE THEN GIVEN A CLOSE PATTERN; BUT BETTER TURN-ON BACK AROUND AND COMPLETED THE APCH PROPERLY. THE NEXT ISSUE THAT NEEDS ADDRESSING IS THE LGA TWR CTLRS' HABIT OF CONSTANTLY CALLING ACFT AS THEY ROLL-OUT ON LNDG. THIS IS GETTING WORSE ALL THE TIME. ON THIS LOW WX NIGHT; HE CALLED US; 3 TIMES; GIVING US CONSTANT EXIT TO TXWY INSTRUCTIONS AS WE ROLLED OUT THIS DARK FOGGY NIGHT WITH STANDING WATER ON THE SURFACE OF THESE SHORT RWYS. WE DID NOT ANSWER UNTIL AT A SAFE SPD AND EXITED TXWY U. DURING HIS CONSTANT 'LITANY' OF ATTEMPTED INSTRUCTIONS; HE TOLD US EXPEDITE ACFT INSIDE 1 MI FINAL; WHICH IS AN ATC SPACING FUNCTION IN IMC WX. LET'S STOP 'BEATING AROUND THE BUSH' ABOUT LGA OPS; THIS PLACE IS HANGING BY A THREAD WITH RESPECT TO SAFETY; AND IT IS A RECKLESS OP EVEN BY 'COMBAT OPS STANDARDS.' THIS ARPT IS WELL PAST ANY RATIONAL MEASURE OF A SAFE OP AND NEEDS TO BE FIXED BEFORE SOMETHING HAPPENS.