B757 CAPT REPORTS UNSTABILIZED FAST APPROACH CAUSING HOT BRAKES AND FOUR DEFLATED TIRES.

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ATC GAVE US 45 DEG INTERCEPT TO RWY XXR IN ZZZ. WE ACQUIRED ARPT SO THEY CLRED US FOR A VISUAL APCH; AND REQUESTED WE MAINTAIN 190 KTS UNTIL THE MARKER. I CALLED FOR GEAR DOWN TO GET US DOWN TO THE ALT AT THE MARKER. THE APCH MODE OF THE AUTOPLT WAS ARMED. I EXTENDED SPD BRAKES TO HELP US GET DOWN. THE AUTOPLT INTERCEPTED THE FINAL APCH COURSE. WE WERE SLIGHTLY ABOVE THE GS AT THE MARKER AND STILL SLOWING TO 190 KTS. THE AUTOPLT WAS THEN DISCONNECTED; AND DSCNT WAS CONTINUED. I FOCUSED ON CATCHING AND THEN MAINTAINING THE GLIDEPATH; KNOWING WE WERE FAST BUT DECIDING TO CONTINUE THE APCH. I EXTENDED THE SPD BRAKES AGAIN TO HELP SLOW US DOWN. AT 190 KTS I CALLED FOR FLAPS 20 DEGS AND SHORTLY THEREAFTER RETRACTED THE SPD BRAKES. FO DID NOT EXTEND THE FLAPS TO 20 DEGS BECAUSE WE WERE WITHIN 5 KTS OF THE MAX SPD. I RE-EXTENDED THE SPD BRAKES; CONTINUING MY FOCUS ON MAINTAINING GLIDEPATH. I CALLED FOR FLAPS 20 DEGS AGAIN. FO SUGGESTED WE GO AROUND. THE GPWS WENT OFF. (NOT IN LNDG FLAPS.) ON SHORT FINAL; FO AGAIN SAID GO AROUND. I CONTINUED; AS I WAS FAST; BUT ON GLIDEPATH. I SAID I'VE GOT IT. WE LANDED SLIGHTLY LONG AND FAST. I HAD SELECTED AUTO-BRAKES FOR LNDG. THE TOUCHDOWN WAS NORMAL; THE APPLICATION OF BRAKES WAS GENTLE AND THE AIRPLANE SLOWED TO NORMAL TAXI SPD BY THE END OF THE RWY. I CHKED BRAKE TEMPS AND NOTED THE R TRUCK HAD HOT BRAKES. WE CONTINUED TO GATE. I CALLED MAINT AND TOLD THEM WE HAD HOT BRAKES. WHEN THE RAMP CREW CHOCKED THE ACFT; I INDICATED THEY SHOULD GET ON HEADSET. I THEN TOLD THEM WE HAD HOT BRAKES ON THE R TRUCK AND TO GET SOME AIR ON THOSE BRAKES. AFTER DEPLANING THE PAX; I WENT TO THE RAMP AND OBSERVED 4 FLAT TIRES ON THE R TRUCK.