I dont see why it couldnt work.

You could say that plaintiff has to pay for a crap lawyer for other side (there are complicated consequences, makes it harder for the little guy to access the legal system, etc). Or you could say the state has to provide one always (if the state pays for my doctor [i am not an american] than its in theory possible for them to do this.

Whether or not they should is a different question.

Probably similar to how it works in criminal trials. There would be a public defender office for handling the civil cases of those without means.

Not saying that it should be done, but implementing it seems straightforward.

In Germany, their rough equivalent of a Civil trial guarantees representation for the sued in most cases.