Bernie is a master of the art of divide and conquer. That is how he gained control of F1 in the first place, by exploiting the teams' distrust of each other. That is also at the heart of the current crisis which stems from the last crisis when the top teams threatened to start a breakaway series a few years ago. Bernie bought them off at the cost of cash flow to the smaller teams. He hoped to manage that by bringing in cost controls but the bigger teams weren't having that!
As the income is unlikely to rise sharply: sponsorship, broadcasting and hosting rights having been milked to the limit, at this point the only way to pass more money to the smaller teams would be for BE/CVC to reduce the amount they take from the sport. It wouldn't have to be a huge amount by F1 standards but it would preserve diversity in F1. That is unlikely to happen, for obvious reasons, so at least 2 more teams will go to the wall and 3 car teams or customer cars will come in. Racing will probably be closer throughout the field when that happens but whether the fans and by extension the sponsors continue to vote with their wallets remains to be seen.