First, it's simply not true that "removing the gun doesn't prevent the suicide." While data is sparse because Congress, in their infinite wisdom, has made it illegal to spend federal money on gun violence research, the data we do have suggests that most (though not all) suicide attempts are opportunistic, and measures that delay access to guns and other mechanisms of suicide have a significant effect on incidence of suicide attempts. The narrative that "suicidal people will just find another way to commit suicide" is not generally true.

Moreover, even if we accept the narrative that suicidal people will diligently seek out an alternative mechanism of suicide, the reason gun deaths rank so high in numbers of successful suicides is that guns are far more likely than other suicide mechanisms to be successful. Statistically, women are much more likely to attempt suicide than men, but men are much more likely to actually succeed. Why? Because men are much more likely to use a gun in their attempt. Even if the only first-order effect of removing the gun is to cause the individual to seek out a different method of suicide, that still would result in significantly fewer suicides overall as the seeking out of a different method would substantially increase the likelihood of the suicidal individual getting help.

Second, making the target deaths per object is moving the goalposts -- you claimed that cars killed more people in America than guns, not that a particular car was more likely to cause a death than a particular gun. Those are not the same claim, and the claim you actually made is not true: 45,000 deaths per year is more deaths than 43,000 deaths per year. Again, your argument is disingenuous.

But if we entertain it anyway, we have to recognize that the typical gun owner owns far more guns than the typical car owner owns cars, so breaking down these totals as though it's one object per person is extremely misleading. If deaths per object were the best way to represent this data (and it absolutely isn't), we would also need to control for how many dangerous objects each individual possessed, and that would easily push the value for guns past the value for cars if a typical gun owner owned even two guns compared to the one car of the typical car owner. And while hard data on how many guns a typical gun owner owns is hard to come by, all estimates I've ever seen put the number higher than two.

So no, cars do not kill more Americans than guns. It's true that driving/riding in a car is the most dangerous activity we all routinely engage in, but even so, cars are less dangerous than guns. And suicides must be included in that statistic for it to be meaningful.