This wouldn't prevent all cases, for sure. Especially cases where there's some merit to the claim. However, for cases where it's 90:10 or 99:1, it'll stop those cases. In those obvious cases it wouldn't surprise me to see more law firms lining up to take the case on a contingency basis. It's easy money and the person that'll pay them is the rich litigant.
The real problem, IMO, is this will disincentivize meritorious lawsuits from poorer people against the wealthy. Perhaps that could be fixed by narrowing the scope of "loser pays" to cases like defamation and libel.
Wouldn't it encourage that strategy? If the case could go either way, the richer litigant can keep increasing the stakes until the poorer one faces ruin on a coin toss. So they are forced to settle. Even if you have (say) a 75% chance of winning, the Kelly criterion puts you out of the game once the expenses reach a certain level.