Would a B61 fit in the weapons bay of an F-35B?But have different roles in the strategic calculus.
Land-based missiles are a first strike weapon. The enemy knows exactly where the silos are, so if you don't launch before enemy missiles impact you will lose your silo ICBMs. The most extreme version of this is "Launch on Warning," where the silo missiles are fired more or less as soon as your IR satellites watching for launch plumes start screaming. A more relaxed version can wait until the long range radars get a track on missiles. About the latest you can wait is ~1min from impact.
Submarine-based missiles are second strike weapons, guarantors of MAD. Because even if the enemy launches and takes out all your bomber bases and silos, there are still missiles with enough firepower to end whichever country launched first. Submarines are very hard to detect, but advancements in underwater detection capabilities makes the guaranteed MAD a little less likely.
Bombers are a very effective external signal of alert levels to your neighbors. People see and hear them, they're tracked on radars from well beyond the horizon, etc. Especially when you have dedicated bombers. It's easier to miss the signals if you only use fighter-bombers.
South Korea was talking about CVN's for their Navy, if they do eventually build any they could be smaller ski jump or F-35B style lightning carriers due to cost and other factors. If the F-35B can deliver nuclear weapons that would give them a pretty good deployment option outside of bombers or land based aircraft that could be taken out in a first strike.
Obvious answer for their deterrence needs would be a nuclear tipped Hyunmoo sub launched missile.