Right. I have always thought of a grazing frame as a larger structure that you place in the chicken run and don't move after that. Hence, I built my big ~3X10 foot grazing frame.

But I'm not too old to consider other options as well, such as smaller, more portable grazing frames.
Here is a picture of a very simple grazing frame you could make out of pallet wood 2X4's and paint them, if you wanted to do that...
I'm sure that would work in many chicken runs. I prefer the natural wood look, but I know many people love to decorate their chicken runs with colorful stuff. What a great way to brighten up the chicken run while at the same time providing something useful for the chickens.
Getting back to the stackable, interlocking compost bin design, I think there would be an extra advantage to having a single tier of the compost bin on the ground with another, maybe shorter, tier on top covered with hardware cloth.
Nothing says that all tiers have to be uniform in height, either. So, for a grazing frame modification, maybe you want those legs only to be an inch high so the potting soil, compost, or topsoil you use to fill the frame does not go falling out the bottom. Or you could push the legs down into the chicken run dirt up to the level of the bottom of the boards.
I am thinking of the top tier with hardware cloth could be moved from grazing frame to grazing frame as you wanted. But nothing wrong with having multiple top covers with hardware cloth either and just leaving them in place on top of the frame.
If you wanted to plant new, or different seeds in any frame, it would be super easy to lift off the top tier with the hardware cloth, work the soil in the lower frame, replant it, and put the cover back on. It's not nearly as easy as that with my 3X10 foot grazing frame.
Later, if you want, you could gather the tiers together and build a compost bin in your chicken coop with those same stackable frames. It's kind of a 2 in 1 solution, giving you more options.

And thinking while I type, why not use one of those same frames and make a dust bath for the chickens?
If you make all those frames with the stackable, interlocking concept, you would have many configurations and options to choose from. I like making stuff that can be used in many ways. The magic in the stackable design is just making those legs in the corners to stack the frames. Of course, the frames would all have to be the same size. But you could use those frames in a number of ways, not just for a compost bin.
Would love to hear about other uses for stackable frames that come to mind. Later...