It's not inherently a problem; it's relatively a problem, given that swapping shares around each other creates no value (i.e. nothing of use to the world has been created), but the rich could instead blow it all on actually creating something or rather, paying for people to do work that leaves the world more actually wealthy (by which I mean, not "has more money" but "has more value"; Bill Gates stumping up cash to help wipe out Polio will leave the world phenomenally more wealthy, but with the same amount of once-owned-by-Bill-Gates cash in it - this is an extreme example of how to do it, but with the very rich it has to be extreme, because unlike poor people, the very rich simply can't spend a significant amount of their money feeding themselves and having a room redecorated and going to the movies).

Also, would it really be so bad if the stockmarket was less speculative and the benefit from owning stock was expected to come in the form of dividends? Everyone would have an incentive to make companies reliably, long-term profitable instead of prone to boom and bust.

Edit to answer the below: Yes, that cash does come from some very wealthy individuals, and what they're doing there is paying for people to do work that leaves the world more actually wealthy (hopefully - if the business crashes and burns when it turns out the world doesn't want shoes that are also electric bananas no new wealth was created). They're hoping to get a lot of that new wealth for themselves, true, but lots of it goes elsewhere too. They're not just swapping shares around; they're actually paying people to do things.