If, hypothetically, every single user used all of their downvotes there would be tens or hundreds of thousands of downvotes per day. The drama will fade away into the ether because let's face it, you can't get upset about something that happens literally tens of thousands of times per day to every single post. If nothing else, fatigue over the drama kings and queens trying to turn everything into a personal attack will set in and people will start ignoring it.
Posts will then get ranked and paid out on the basis of which have a more favorable balance of upvotes and downvotes. Some people will upvote stupidly and some will downvote stupidly but mostly that will cancel out and the sensible application of upvotes and downvotes will prevail (unless the majority of the user base and stake are simply stupid, in which case there is no solution). I could not think of a better outcome.
Downvotes are current a big deal and drama today because they are so rare. Whenever it happens it is seen as a personal attack rather than an expression of opinion.
In reality I do not expect everyone to use all of their downvotes, so the favorable outcome described above won't happen, unfortunately. Hopefully we can end up somewhere in the middle.