Everything happening around us indicates the opposite: that the rich prefer to invest in that which gets them richer, not that which benefits society.

Don't some investments benefit society? For example: Invest in real estate that turns into housing or businesses that weren't there before, or investing into businesses so they have the money to grow to a larger building or hire more people to meet demand.

Well, sure. It's easy to say some investments benefit society, but most of the time they are solely for the benefit of the wealthy.

One just needs to look at the land stratification California has been going through to understand why. Most of the issues they face are a result of the wealthy doing everything in their power to prevent land from being upzoned or rebuilt because that devalues their property or ruins their view.

In this case there's no growth happening despite a desperate need for growth because the wealthy don't want it.

A land value tax would fix this - the more land appreciates in value, the more property tax the owner would pay to the public coffers. California would also have to repeal proposition 13 which limits property tax increases. Proposition 13 is one of the biggest giveaways to the wealthy in the history of US tax policy.

Taxes on income and taxes on investment gains should be the same. In the UK, a 20 year old contributing to society by doing £45k worth of work every year keeps 69% (£30,737)

Meanwhile a 70 year old seeing their BTL property appreciate by £45k a year due to crossrail (paid for out of income tax the 20 year old is paying) keeps 87% (£39,060)

Isn’t this a restatement of trickle down economic theory (sans raising inheritance tax), which has not really panned out when attempted?

The problem with trickle down economics is that it involved decreasing the taxes of the wealthy so that in theory that money would trickle down to improve the lot of the poorer.

This doesn't work because the rich can opt to do a lot of different things with their money including hide or invest it overseas.

Taking the money of the rich and using it to directly improve the lot of the less fortunate has been tried and actually works as one would expect.

My understanding of trickle down economics is that you get more economic activity by putting a dollar in the hands of the bottom 10% than the top 10%, which makes sense since the propensity to consumer is higher at the bottom. By investing, the top % supports invention and innovation. By consuming, the bottom % validates those inventions and innovations that are worthwhile, versus those that are worthless. Both functions are required in order to keep the economy humming along producing and consuming new goods and services at a rapid pace. There would seem to be some function which maximizes the utility of each group in their respective roles. That's what I would want tax policy to reinforce.