While there is evidence that RFK's position was more hawkish initially than he let on in "Thirteen Days", the fact remains that an invasion would have gone very badly if the Soviets used the tactical nukes now known to have been deployed in Cuba. There were two primary invasion sites, one east of Havana and one west, per this map. So, unless airstrikes took out the missile sites before the invasion, there's a good chance of complete failure. The invasion could fail and the attempt to take out the missiles would fail. The next step for the US would be escalation to the use of nuclear weapons to take out the missile sites with all the possible consequences that could have including a Soviet attack on the US with nuclear weapons, the use of Soviet nuclear weapons on US naval assets around Cuba or a general Soviet move in Europe to take West Berlin and/or an invasion of West Germany. While we now know that there is a very decent good that the US would have survived a general nuclear war with the Soviets in 1962 (the USSR had few missiles, turboprop bombers and little to no SLBM capability), survival does not mean unscathed. Meanwhile, Europe and the Soviet Union (and probably China) would have been damaged or thoroughly destroyed and there's a good chance US allies in Asia (Japan, S. Korea, the Philippines, Taiwan) may have also been damaged.
The only thing that probably would have worked to get rid of the missiles with something approaching certainty was unthinkable: a surprise first strike with nuclear missiles on Cuba directed at the missile sites. There were ample tools for this: land-based missiles, SLBMs, bombers or air launched stand off missiles. The problem with this was what made it unthinkable: no certainty of what comes next from the Soviets and a very real chance that it leads to general war.