It seems like we should switch from the academic model to a system of funding based purely on vibes.

The supposed problem is that organizations behave too predictably. But billionaires can use their ill-gotten gains to fund whatever they like, which is a good thing—solely because of the random variable.

I'd accept that the allocation of public research funding can be too conservative.

However, billionaires are more likely to buy a yacht than spend money on research that isn't immediately commercializable and directly connected to their business. You can find examples of billionaires spending money on unlikely research that actually paid off, but how much more fantastic research has failed to occur because of bad tax laws? i.e. When the Jeff Bezos' of the world pay less income tax than school teachers, the resulting loss of tax revenue starves publicly funded research.

Unlike the sexy and quick to gratify research a billionaire is likely to fund, publicly funded research can be long-term and curiosity driven, with no payoff in sight. This is the kind of research that lays the foundations for new fields.