Billionaires already represent societal detriments by the very nature of the absurd concentration of wealth into the hands of an individual.

Also billionaires tend not to personally manage things, which may be to save time for doing more abuse (see Elon)

Society already pays many taxes and changing the spending doesn't happen freely by society.

Much of what those taxes are currently spent on is utter bullshit for oligarchs

billionaires are a complementary way to allocate resources.

[citation needed]

That society can be locked into Twitter shows that taxes shouldn't be the only source of capital. Every democracy could have created a Twitter clone many years ago as basic infrastructure.

China facilitated conditions for the creation of such clones quite well. America's cultural imperialism had already dominated Europe anyway and neocolonial infrastructure pushes many third world countries towards western services being synonymous with the internet itself. The market solution is for the dominant power to snowball, with all the problems that entails.

Politicians rely on society for sustainability whereas billionaires have to identify and improve sustainable forms of income.

This is a joke. Aside from the politicians being bought out by those self-same billionaires, the latter are infamous for making things worse long term (or just in totality) in order to maximize quarterly profits, again see Twitter. They burn money on bribing politicians and institutions and drain society of wealth with various forms of tax fraud while paying hardly a cent for all the infrastructure that they use in wild disproportion to a normal citizen.

If neither politicians nor billionaires should invest, what would be a good way to identify the people who should?

My point is that it should not be oriented around one person's executive decisions: Stop looking for a good king. It should be decided democratically or, at the most republican, by a representative who the laws are oriented around preventing the corruption of (no lobbying, PACs of any kind, "campaign donations" from anything but a private citizen, no "gifts" at all, no revolving door employment, no "speaking fees") who also is subject to a vote of no confidence or some equivalent procedure that allows the citizenry to terminate his term early (and put him on trial, if needed) if they find him to not be acting as he represented that he would. But all of this is to say it the representative should have as little personal agency as possible in day-to-day affairs, merely acting as a laborer performing tasks according to the lines the public wants him to without needing to have the entire citizenry be up-to-date on everything all the time (as they would need to be in a pure democracy).