ACR LGT MADE GO AROUND WHEN UNABLE TO GET LNDG CLRNC DUE FREQ CONGESTION.

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WE WERE GIVEN THE USUAL APCH TO LAX BUT NOT CLRED VIA THE PROFILE. WE HAD SPD CONTROL. WE WERE KEPT HIGH 18000' TO 40 MI FROM LAX; THEN CLRED TO DSND TO 4000'. THE LGT WAS CONFIGURED TO BRICK MODE AND WE WERE DSNDING AT 4500 FPM 230 KTS. AT 4000' APCH CLRED US TO 2000' AND A MINUTE LATER TOLD US TO MAINTAIN 2000'; CONTACT TWR. WE CALLED/TRIED TWR AND DID NOT GET A RESPONSE NOR WERE WE ABLE TO BREAK INTO THE CONVERSATION. WHEN A LNDG COULD NOT LONGER BE ACCOMPLISHED I EXECUTED A MISSED APCH FROM 2000'. WE COULD NOT BREAK IN TO NOTIFY TWR UNTIL WE WERE AT MIDFIELD AND SEEMED TO BE A SURPRISE VISITOR AT LAX. AFTER SOME CONFUSION BY THE TWR AS TO WHAT WE WERE TO DO; WE WERE GIVEN A HDG; ALT AND TOLD TO CALL DEP. DEP SWUNG US AROUND TO THE N; TURNED US E AND GAVE US TO APCH. APCH TURNED US DOWNWIND AND; WHEN WE WERE ABOUT 5 MI E AND HAD THE FIELD; CLRED US FOR THE VISUAL AND TOLD US TO CONTACT TWR. TURNING TOWARD LAX RWY 24L TWR TOLD US TO SLOW TO MINIMUM SPD AND SQUARE THE BASE AS THEY HAD A WDB ON THE RWY AND NEEDED WAKE SEP. WE COULD NOT BOTTOM HOOK THE FINAL AS RWY 25 WAS IN USE AND SHOWED DOWN TO VREF +5 AND TOUCHED DOWN BEFORE THE 747 ROTATION POINT ON THE RWY TO AVOID WAKE TURB. WE FELT SOME ENG/EXHAUST TURB. AFTER LNDG AN ANONYMOUS VOICE CAME ON THE FREQ AND SAID; 'WELCOME TO LA.' THE PROBS CONTRIBUTING TO THIS WERE AN OVERRUNNING EASTERLY FLOW OF 35 KTS. LNDGS WERE MADE WITH 5 KTS DOWNWIND. THE ADDED GND SPD WAS BRINGING TFC TOWARDS THE ARPT FASTER THAN NORMAL. IN ADDITION; WAS THE RAPID FIRE SPEECH OF ATC W/O ALLOWING A SPACE FOR ACFT RESPONSE. IT SEEMS EVERYBODY IS TALKING TWICE AS FAST AS A FEW YRS AGO. THERE SEEMED TO BE A BREAKDOWN IN ATC TO TWR COM AND IN TWR PROC AS ALL ACFT WERE EXPECTED TO LAND AND NO CONSIDERATION WAS MADE IN THE MINDSET FOR A MISSED APCH. WE WERE VISUAL AT ALL TIMES AND IF WE HAD EXECUTED THE PUBLISHED MISSED APCH PROC WE WOULD HAVE BEEN CLOSE TO A DEP. SO WE MAINTAINED VISUAL AND PROCEEDED STRAIGHT OUT AT 2500'.