MULTIPLE RWY OP PARALLEL RWYS CPR X TCASII RA FROM ACFT Y LNDG ON PARALLEL RWY EXECUTED GAR.

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CPR X ON VISUAL APCH APPROX 1.5 MI FROM RWY 36L STRAIGHT IN. ACFT Y WAS ON R BASE LNDG RWY 36R. TFC WAS POINTED OUT TO EACH ACFT. CPR X THEN STARTED A CLBING L TURN AND STATED HE WAS GOING AROUND. I ASKED THE PLT IF HE WANTED RESEQUENCING WITH MSY APCH OR TO MAKE L TFC FOR RWY 36L WITH NEW ATCT. HE CHOSE L TFC; THEN ADVISED ME HE HAD RECEIVED A TA. THE RA ADVISED TURN L; AND CLB AT 1900 FPM. HAD HE DONE THIS HE WOULD'VE OR COULD'VE COME VERY CLOSE TO INBOUND TFC TO MSY XING NEW ARPT AT 3000 FT MSL. ALL COORD WAS COMPLETED WITH MSY APCH AND NO AIRSPACE VIOLATION OCCURRED NOR WAS SEPARATION BTWN ACFT LOST AT ANY TIME. TCASII USE IN THE ATA WHERE SIMULTANEOUS SAME DIRECTION OPS ARE AUTHORIZED MAY CAUSE MANY MORE INSTANCES SUCH AS THIS; WHICH COULD'VE ENDED A WHOLE LOT WORSE. IN LESS THAN A MIN; CPR X IN RESPONDING TO THE TA (TCASII) WOULD'VE BUSTED SEPARATION WITH AN AIRLINER ON APCH TO NEW ORLEANS INTL ARPT. NUMEROUS ACFT INBOUND AND OUTBOUND TO MSY CROSS OVER LAKEFRONT ARPT DAILY AT 3000 FT AND WITH THE INCREASED USE OF TCASII THIS COULD EASILY HAPPEN AGAIN.