> But, by my understanding, the sarcomeres, which are the source of the actual movement, don't run end to end, they're chains.

It doesn't really matter, except the not being homogenous end-to-end means it's the weakest point that matters. But, irrespective of the structural details, there is some force in the direction of contraction that will cause failure, and that force is proportional to, basically, the number of linkages it is distributed across in parallel (not connections in series, such as along the chain) which is proportional to cross-sectional area.

> The entire line of reasoning seems to rest on the idea that the smallest unit we consider runs from one end all the way to the other.

It is not (in fact, the entire reason it is true of any material is because even structures which seem to be end to end are composed of smaller structures with fallible linkages; if there were indivisible end-to-end structures, this would cease to be a concern.)