re: Could most legal cases be solved without a lawyer?

You focus on traffic / criminal matters… here’s what I’d say the bottom line is in such cases: you can either negotiate a settlement / plead down, or go through a hearing.

Many cases are on these dockets, so the DA (& Judge) want to move efficiently. The DA doesn’t really want to talk to you on your own. They’d much prefer to speak to your lawyer.

Thus, your only shot (unless you want to plead to the charge filed) is to represent yourself in the hearing. You likely will not prevail.