There's a HUGE problem with that strategy: it's not just a tsunami against Trump, it's also a tsunami against courts whose judges don't appreciate it and who have broad authority to react as they see fit.
Even judges who might tend to rule against Trump might be swayed the other direction if they feel like they are being used inappropriately as this sort of strategy.
In short, a strategy like that feel good but actually end up being quite counterproductive, giving Trump a bunch of wins in courts as the judges dismiss challenges to deal with the sudden flood of filings.