Blockading and besieging Japan would not make the fanatical Japanese to surrender at anytime. We blockaded Japan for months before August 1945 but still haven't persuaded the Japanese to surrender. The siege of Leningrad lasted for three and a half years which killed millions of civilians but the Russians still haven't surrendered. Admiral Chester Nimitz stated that blockading Japan would not only starve the Japanese people but also exposed their naval ships to kamikaze attacks. As long the Japanese have their own land unoccupied by the enemy, they would keep continue to fight to the death, no matter what the cost. We knew how fanatical the Japanese were as demonstrated in the Battles of Iwo Jima and Okinawa. In Iwo Jima, 22,000 Japanese troops defended the island. Of these, 20,000 were killed and only 216 were taken prisoners. The rest of Japanese casualties were listed as MIA. The Battle of Okinawa was the first and only battle in the Pacific War where civilian deaths exceeded those of the military. An estimated 72,000 Japanese troops, 12,000 U.S. troops, and 150,000 civilians were killed during the two-month battle. The reason why there was a high civilian death toll in Okinawa was mostly because civilians were forced to fight the Americans, killed by their own military in fear of spying, and committed suicide by the thousands in fear that the victorious Americans would rape them after the battle. The invasion of Japan would dwarf the numbers that could have the equal death toll comparable to the casualties in the Eastern Front.
The only way to force Japan into surrender was the invasion of Japan. The invasion would no doubt forced the Japanese to accept an unconditional surrender but would cost millions and millions of American lives along the way in an already six-year war. The invasion of Japan would have extended for one or two more years. By 1945, WWII had cost 400,000 American lives and almost crippled the U.S. economy to the point the American people were tired and demoralized that unconditional surrender demand might be dropped in favor of conditions endorsed by Japanese officials.
That's why with a new and revolutionary strategic weapon (i.e., nuclear weapon), we decided that using this technology, it would shock the Japanese into surrender and show them the new deadly arsenal we have had for the enemy. Two nuclear weapons were used against the Japanese cities of Hiroshima and Nagasaki, killing 140,000 civilians and military personnel. The intent was to show the Japanese we can destroy a city with a single nuclear weapon in a far increasing rate as opposed to 400-500 bombers armed with 1,000 tons of conventional firebombs. While the death toll in Hiroshima and Nagasaki were horrific, these bombings were nothing compare to what the invasion of Japan along with blockading and besieging would have cost.