That's assuming you are the one doing the suing and not the one getting sued. And even then, that applies to only very limited types of cases. And even then, the contingency is typically 33% (and sometimes can even eat over 50%) of your damages awarded, so the cost is massive in any case.

There is the option of small claims court which is massively cheaper, but it has very low limits for damages, so it's barely worth the effort.