As Goran and Bob showed you, there is a big difference between securing a Hobie 18 and an A Class.
The A Class need to be stored on their dollies or trailers. Not only because their hulls are thinner but also because a scratched up A Class is slower (and so tacky).
The lever effect they refered to is due to the light weight. A Hobie 18 with 50 lbs of force against the mast due to wind is nothing, but a 50 lb force against an A Class mast can flip it. Even if facing the wind, an A Class wing mast could generate enough lift, in the horizontal direction, to flip it. This is usually the cause of the "dancing" you mentioned. It is not usually related to wind on the platform. This is similar to "buffeting" in a plane. By tying off the trap lines, they stopped the horizontal motions, occillations, of the mast.

Anchors
I carry two types with me, the spiral screw (dog anchor) and the plate-type trailer anchor, (redneck insurance policy).
The plate-type work best when you can get them in the ground. Mine have a plate about four inches in diameter. This is usually OK, but can pull out of soft sand. I would like to get a pair of the ones with the eight inch plate. I use the spiral anchors when the ground is too hard for the plate anchors but the cheap ones can break easily.

Assuming you have a securing tie down, how the boat is tied can make a big difference.
Most of us just have one line up and around the mast step. This can allow alot of horizontal movement and damage.
There should also be a tie down at the reacrossbar too.
Even on a heavy boat, the mast should be tied off to prevent rotation and take out any slack in the shrouds.