Trivia: Ken Watanabe is named "Dr. Ishiro Serizawa." His first name "Ishiro" comes from the director of several previous Godzilla films, Ishiro Honda. The last name "Serizawa" is the name of the character in the 1954 original film who invents a device to kill Godzilla, Dr. Daisuke Serizawa.
Trivia: This movie came out in 2014, 10 years after 2004's Godzilla: Final Wars. In a way, this movie helped keep Final Wars' promise of being the last Godzilla movie for at least 10 years.
Answer: Because detaching them and reattaching them would have taken time, which they didn't have.
But, after the crash, they remove the warheads and transport them by helicopter and leave the boosters behind, as they only need the warheads.