So far it seems that the biggest passenger growth happened within the leisure traffic segment, and indeed it was already known from previous studies (including some smaller scale recent-ish experiments in Germany) that commuting traffic in particular is more sensitive to reliability and journey time and not
that extremely price sensitive.
I'd think that commuting is simultaneously the biggest driver behind the decision to purchase a car or not, so all in all that leaves me rather sceptic on whether you'd really get people to abandon their cars en masse that way.
I'm also sceptical on the political willingness – silently and behind the scenes, some states (Hessen, I'm looking at you) have actually right now reduced their public transport budgets in order to make up Corona-induced budget holes. So the "true national through-ticketing for all public transport"-aspect of the 9 €-Ticket was nice, but beyond that I'd personally still rather see any money that can be scrounged together beyond that to be spent on service and infrastructure improvements. (And what with the staff shortages and energy price increases and possibly a recession on top we might even have to worry about even maintaining current service levels…)