[wongarsu]

At any fixed distance from the sun there's only one speed where you have a stable spherical orbit. Since actual spheres have poles that don't move much at all, any dyson swarm that approaches a sphere has to consist of parts in a number of different orbits. That's inconvinient for a whole host of reasons (sun often occluded as segments move below you, movement between segments is difficult etc.). In comparison a swarm that looks like a narrow ring has no such problem: everything is approximately at the same speed while traveling in the same direction. For that reason alone rings are the superior choice regardless if your structure is solid or a swarm of independend objects.

Maybe multiple rings would form for political reasons, but that just makes the individual rings proportionally thinner.

[logfromblammo]

I was under the impression that Dyson sphere participants would be mainly heliostats, whose station would be kept by balancing their inward gravitational attraction against the outward pressure from reflected or decelerated solar wind.

Whenever an object would intersect the sphere, the nearest heliostats alter the angle of their mirrors/sails to drift away and make a hole. Then they drift back to close it after it passes.

There's nothing to say that they can't also have an orbital velocity component, as it takes quite a lot of delta-v to decelerate from a near-circular solar orbit, and orbital velocity can make up for lack of sail area.