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Street drains, like those in your kitchen sink, are designed to let water and small amounts of solid matter pass through. Beyond that, they will clog. Their design demand it.
How about street drains with gradual "convex" rises instead of straight bars. They would be strongly built to withstand cars and trucks. Leaves, paper, and other debris would shed from the top of the drain and sucked to the lowest open areas. Water, blocked by the forming debris at the base would be forced to seek a "higher" level toward the top of the drain and through.
Yes, this drain would also eventually clog, but not with moderate amounts of debris.