This was something Louis Rossman suggested at one point. Small claims courts don't typically allow lawyers and require a direct representative. And small claims courts are fairly cheap financially and judicially to file in.

I wager such an attack would be very costly since they'd likely be ordered to pay the court cost of around $100 per case if they left it to default. But if they didn't, they now need to take an employee from somewhere to represent them instead of doing their actual job, which is also costly. So getting even 100 people to do this simultaneously could cost upwards of $10,000 to the target company.