The only advantage in ALBM had over an ICBM is second strike capability, but an SLBM is even better for that.
During the Cold War, the Soviets had plans to use nuclear-armed ballistic missiles against American carrier groups. There was an inherent problem with locating the target prior to launch, but the Soviets had a lot of submarines and figured that even if one was destroyed after getting a message out, it would be worth it. A conventionally armed ballistic missile will have problems with terminal guidance because radar waves can't go through the plasma sheath that forms during reentry. The Chinese anti-ship ballistic missiles use maneuverable reentry vehicles to slow down to the hypersonic flight regime so they can use radars, but that also makes them an easier target for surface to air missiles.
My understanding is that this was similar to the big Soviet anti-ship missiles and to the Phoenix air to air missile. A lot of long range missiles have a flight mode that takes them up to 80k to 100k ft, which allows them to cruise with much lower air resistance. They can't use aerodynamic controls at this altitude, so the trajectory between the stratospheric entry and exit points is ballistic unless the motor is still providing thrust.