Is wealth inequality actually a problem I have been searching around online, but cannot really find an answer to my question.

I can find a lot of material covering wealth inequality and how it has developed over time, but haven’t found any material to support my theory (or the opposite).

My question is: Is wealth inequality actually a problem? With this I mean the super wealthy vs the rest (if that makes a difference).

I will try to explain my thinking as good as possible. My theory is, that super wealthy people tend to not spend all of their money, they may invest it or set it aside.

Consider a scenario where an individual owns 99% of all the wealth (i.e. money, disregard stocks, bonds etc in this scenario) in an economy, but spends roughly the same as everyone else in the same economy, effectively “disabling” a huge portion of the wealth. Would the “poor” actually be affected by this negatively? Would prices on goods reflect that “effective” wealth, or the total wealth in said economy?

Another scenario could be where one person owns most or all shares in all companies in the economy, and everyone else living of of salary. Would this actually be a problem? I imagine that it is same as above scenario.

Obviously these are silly extreme scenarios, I was just trying to paint a bit clearer picture of where I am coming from.

If the super rich (or perhaps top 1%) have an average spending similar to everyone else in an economy, with the only difference that they own more wealth, would that actually be a problem; or perhaps in reality a smaller problem than how it is depicted in the media?

I am not looking for political standpoints, but a more fact based answer.
I think that you are more or less than correct in thinking that cash that is never spent (nor expected to be) may as well not exist. Thought experiment: suppose that, unbeknownst to you and everyone else, £1 million suddenly appears under your mattress. If you never discover the money, it is hard to see how it could change anything in a meaningful way.

There are some caveats, however. First, a game theoretic point: even if rich people never spend their money, threats to spend their money might influence outcomes. For example, they could pledge to donate lots of money to the political opposition unless the government does what they say. If this threat works, they will never need to pay out.

Second, a ‘non-economic’ point: money gives you options, and people might enjoy having options in itself (even if they don’t spend the money). One might object to the kind of ‘options inequality’ brought about by an unequal wealth distribution even if rich people never spend their cash.

Third, to bring us back to the real world, we should stress that, usually, rich people do consume more than poorer people. So while it might be interesting to discuss wealth inequality without consumption inequality, this is not a phenomenon which we are actually facing today.