As for whether "the rich gaining large sums of money doesn’t matter much either" - if you're asking if it doesn't matter much either to them then yes, this is the flip side of the marginal value of money point. A person with $1000 in the bank will be much happier about getting extra $100 than a person with $1M. It's one of the core (if not the core) argument towards reducing income inequality - moving some money from the rich to the poor is a net increase in happiness and value in society.
One strong caveat being, building things that require big capital expenses, like factories or specialized machinery or infrastructure. These things require being able to front up a lot of money, and at the same time, they don't mesh well with democratic decision-making. So you want to have some way in a society for an individual, or a small group of individuals, to be able to take control over large amounts of money - otherwise factories and bridges and utilities just won't happen. This doesn't necessarily mean you have to allow that small group of people to capture the entire wealth they generated, though.
Will they, though?
Going by absolute value, perhaps, but that's nowhere near the whole story. Yes, if owners of a megacorp lose $100M, they've lost more than all their employees combined - but they still have a $1B between them in other assets, offshore bank accounts, whatnot, so they stay rich, while their employees suddenly find themselves in a life-threatening emergency.
I can't think of a single market crisis that kicked down the richest people to the level of the poor. Wars and revolutions, yes, but not a market crisis. The more money you have, the easier it is to protect it - and marginal value of money grows sublinearly, so losing even 50% of your wealth hurts less the bigger that amount is. On top of that, connections and networks don't go away in a crisis. Which brings me to:
> during the rebuilding a different set of people will gain the upper hand and end up on top
One way for a competing upstart to get ahead of the other upstarts would be... to hire some of the "old guard" in advisory roles. After all, the crisis doesn't suddenly invalidate the ex-top people's knowledge experience. On the contrary, not only they still have relevant experience that an upstart doesn't, they also have benefit of hindsight and connections. So while the names of the companies and their CEOs may change, I'm pretty sure many of the old players - ones that didn't choose to retire and enjoy their riches - will quickly find their way back into the game.
As for their employees, maybe they'll find their way back to their original positions too. Some day. After they dig themselves up of debt. That is, if the experience of having to give their kids heated ketchup packets for dinner didn't completely break them.
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EDIT: To be clear: revolutions and wars aren't the answer either. A big enough wave of death and destruction will be enough to grind down the richest too, but that's only a way to re-roll the dice on who's the rich and who's the poor in the next round. And the poor, again, suffer disproportionately here.
For some reason this is seen as controversial these days, but I honestly believe that stability is something that works in favor the poor, not against them. It limits what they can do (the dreaded "status quo"), but it also puts a limit on losses. As long as the society is stable, we can try to make steady adjustments, even if it's a grind. If it starts to collapse, everyone enters survival mode, and everyone is much worse off. Even those who survive the chaos and chance their way into the top will have to live in the smoldering remains of their previous civilization, which is almost surely worse than what they had before.
(Worth remembering we all have more to lose now. 1000 years ago, life before and after war wasn't much different. 70 years ago, the difference was stark. Today, it would be greater still. All the quality of life we enjoy today is very far from "ground state" of humanity, very quick to undo, and very hard to restore.)