The thing is, in years gone by, Dear old Bernie, while wanting as much cash as possible, deep inside that black heart, genuinely loved Formula 1. The other blocker on breakaway reforms were the remaining grandees such as Frank Williams.
F1 is in a very different place today. There is almost no one left from the "old days". Liberty have no ingrained love of motorsport, they are a media company who want to maximise global viewership and generate revenue in any way possible.
Finally, the FIA have no authority or leadership to control all the pieces on the board. The FIA needs F1 far more than the other way around. There is no longer any threat from the FIA regarding things they could block such as the use of their tracks for breakaway events. When we are even discussing at higher levels, Monaco could be dropped, it shows Liberty don't care where they race as long as there are races.
All Liberty needs to do is tell the teams under a breakaway they'll get increased prize money and a raised budget cap and there will be a lot of support.