Not unless the bottom 99.99% take action. As most already suspect what this research shows, the sad answer is: No

It's not a 'proof', it's a statistical study, and econometrics rarely convince anyone of anything.

Is it possible that it moves the Overton window? I mean, in the US there has been serious funding for decades aimed at moving the needle around things like guns and taxes. And that organized long term effort has been very successful. Possibly some of these things may result in some swing back to the middle?

If you had a free market, then the rich would either invest their money or they would lend the money out at a reasonable interest rate. The latter doesn't actually happen because they also have the option of simply holding onto it if nobody borrows it. (Of course in fractional reserve banking new money is created with every loan but the lender's money is out of circulation).

Money has an insurance effect. Simply having money lets you pay off random expenses. It also doesn't spoil like goods. If we had a grain money system, then the central bank would pass the cost of grain storage onto the holder of the dollar bill which would give the lender an incentive to lend it out even at 0% interest, which protects the lender from the storage costs. This is known as liquidity preference. The borrower has to compensate the lender for giving up the liquidity benefits of money.

Right now cash itself has no storage costs, so nobody will lend it at 0% interest.

In theory giving the rich money through lower taxes lowers the interest rate because they lend it out. However, as I said, there is no mechanism that actually lets it fall to 0% (extreme cases like deflation can in theory justify negative rates). If you were to charge a negative interest rate on a bank account to enable 0% loans, then people just pull their money out and hold cash instead.

The free market basically ends the moment markets are saturated and everything only makes enough money to cover its own costs with 0% profit. This is one of the areas where Marx was correct. Once profit is gone, the system collapses because someone forgot to enable the 0% interest feature of money.