If we killed all billionaires, would that destroy capitalism or would their money just get transferred to their successors?

That's a weird question. Of course it would be inherited by their successors. I don't know if I understand the question.

Their assets would be inherited and production would continue, simply business as usual. Nothing would change in the big scheme of things for two reasons:

1. Billionaires are not needed for production. They're literally useless. They are leeches that steal the value workers produce. They are not needed for production to go on.

2. If the mechanisms of wealth accumulation aren't disrupted, new billionaires will appear.

The problem is not the individual billionaires. The problem is the existence of bourgeoisie as a class and their private ownership of the means of production, through which they capture and accumulate the value that we produce through our work.

Even if their wealth is not inherited you'd still have capitalism. Suppose a crazy government killed all billionaires and redistributed all their assets. Even in that case, if private ownership of the means of production continues, surplus value accumulation will eventually produce new billionaires.

You'll never see serious Marxists advocating for polítical assassinations as a strategy. Because it's pointless. They know that the problem isn't specific individuals and their morals, but the mechanisms. Those mechanisms produce a class of individuals who can accumulate power and wealth by controlling other people's work. The only solution is eliminating this mechanism and turning those people into regular workers.

In the late 19th century oppressed Russian workers managed to assassinate multiple magnates, ministers of state, and even managed to assassinate Czar Alexander II in 1881. You know what this accomplished? Absolutely nothing but increased oppression and vigilance. Because the problem isn't individuals. It's how we collectively organize around production.