True of Soviet ICBMs (including some still operational in Russian service) and early US ICBMs, but the Minuteman I, introduced in 1962, and all later US ICBMs (Minuteman II & III, Midgetman, Peacekeeper) were solid fueled.

> and could be launched straight away but had other issues

Those “other issues” directly impact the probability of successful launch “straight away”, and did involve having to replace the fuel. (They also involved missiles exploding in their silos, which is bad enough when it's a ground based ICBM, but pretty catastrophic when it's a sub-launched ballistic missile, which cost the Soviets a number of subs apparently.)

To be fair, there were Titan II's in service almost until the very end of the cold war; into the late 80s. (And were used for satellite launches until 2003, but that's another matter.)