2D clusters

I have seen all this discussion about "ring worlds" and I am wondering
why a 1-D structure would be preferable to a 2-D one.

Lets first make some computations about a geosynchronous ring world.
Imagine colonies 10Km in diameter at 36,000 Km altitude, following a
circular orbit with a radius of 42,400 Km. Supposing that each colony
is 20 Km from its closest neighbors to the left and to the right, then
there would be over 13,000 colonies in this ring.

However, those same 13,000 colonies could be arranged in a grid of 115
x 115 cells. If each cell has 20 Km in side, this is a square of 2,300
x 2,300 Km . I am imagining a *physical* grid, made of beams 20Km long
connected to each other in 90 degrees. Each colony would be attached
to each joint point of four beams (using some kind rotational joint,
like those in the pairs of O'Neil cylinders) and there would be rails
in the beams, so that transportation between colonies would use
special pressurized "trains". This would be a physical structure and
so distance between colonies would never vary. Half the colonies would
rotate in one direction and half in the other, so that the overall
angular momentum is zero and the structure does not rotate - I imagine
it kept aligned to the Sun.

Now the obvious objection to this would be tidal effects from Earth,
which would indeed happen if this thing were in geosynchronous orbit.
However, putting this Grid in a Lagrangean would likely minimize tidal
effects to very tolerable levels - and the structure itself could be
designed to bend a little to comply with the feeble tides.

I even thought about putting this structure not in L4 or L5, but
rather in L1, were tidal effects would be *really* negligible and the
structure would be eternally in sunlight. However, I am not sure how
much dynamical stabilization is feasible (economically and physically)
for a structure this size.

Does anyone see anything wrong with that idea?