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As for the tires, nobody is saying you shouldn't put bigger ones on. They would be fun and give a better ride off road, but in order to make up for the larger size, you would need a larger axle sprocket.
Otherwise you will just burn up the clutch and have really shocking acceleration, which at times can actually limit your top speed, if there isnt anywhere big enough to hit top speed then the lack of acceleration is useless.
As for the sprocket clearance issue, another way around it more or less is to have the sprocket right up against one of the tires, unless you slid off the edge of a sharp rock or something you will never hit the sprocket because its always at the same clearance as the tire.