Russian drum-beating at the time, foretold of a carrier on a par with Enterprise and also nuclear powered. Kirov and Frunze were laid down at the time to be her escorts. The USN dithered with killing it and then President Carter cancelled the B-1 in favor of a long range missile that could do the same thing as a bomber. The Navy jumped on the funding wagon and soon, ALCM/SLCM were born. The Navy's purpose for building it was always conventional. The USAF's was to give life/punch/power to the ageing B-52 fleet. After hearing Carter's reelection speech in person, the gist of USAF ALCM was always going to be nuclear. And at a range of 1500+ nm, not too shabby. The slow speed was derided by the Navy but lovers shouted down the haters by preaching that they would "flood Russia with them, so that the Russians wouldn't have enough planes to shoot all of them down." Hmmm...
Basing the shell on ASROC and indeed the launching mechanics, the USN quickly adapted it's trial rounds for submarine launch and BGM-109A was born. It was a small family with A being the nuclear 1200 nm range tactical nuke, B being the 2000lb warhead anti-ship/carrier bird and C being the one that flew down the length of the runway spitting out submunitions. A suitcase with the nuke tools made its way onboard the SSN's and that way any of the B's could be so-configured. The Navy's initial B test was vicious and sank the target ship in record time with one round. SUBDEVGRU TWELVE did the honors with either Dallas or Groton being the "bearer of bad news." The next B test was shot against a CIWS armed ship that failed to shoot it down. CIWS and host went to the bottom. A C test was ordered and tore up a healthy chunk of Point Mugu.
Publicity wise, the first the USA would know of it was Carter's reelection bid and the USS New Jersey with her eight quadruple B and C launchers. Long Beach and the Virginia's got 'em and a handful of Sprucans. The next public outing of TLAM would be the vertical launch Sprucans and Tico's. Once Reagan reached office, the B-1 was back on the drawing board and the TLAMs went away in favor of the revolver launcher SRAM which is specific to the B-52 and B-1 only. During Operation El Dorado Canyon and Operations Prarie Fire I and II in the mid 80's, SSN's attached to the units "may" have launched some at Libyan/Iranian units/targets but that can't be confirmed or denied.
Flight II and III boats launched TLAM C's at Iraqi airfields during Desert Storm and Louisville launched the first TLAM B which was a reworked BGM-109B converted from anti-ship to bunker busting. Other than that, the sub fleet's been pretty sparing with them though British boats so-equipped fired them during OIF.
ASROC was nuclear tipped and served one purpose; to kill an enemy boomer. It was pretty much a suicide weapon as the noise it made leaving the ocean pretty much gave the shooter's location away. Like a lot of Cold War weaponry (ASTOR, Weapon Alpha, Davy Crockett, etc) it was retained only to make the Soviets think that it worked and cause them to spend themselves into oblivion trying to counter it. Tullibee's nickname was "building 598" as she rarely got to sea, if at all. Her propulsion system was just so hopeless.