The rule here, the Seventh Amendment, confers a right to a jury trial when one would have been required under English common law at the time the seventh amendment was written. Roughly speaking, in the English system, cases involving monetary damages were handled in courts of law with juries. Cases that involved injunctive relief (orders to do or not do something) were handled in courts of equity with decisions made by judges.

How is it beneficial to not require extra public burden to complete cases when the issues justifying that burden are resolved without trial?

Or how is it beneficial that issues get resolved without trial?

Because I think both have clear benefits in general.