> Assume an arbitrarily high coefficient of friction between all surfaces

Yes but in practice that means using glue, at which point you might as well glue everything together into a single piece.

The difference is that glue can withstand tension which changes a lot. Even infinite friction still requires a non-negative contact force (i.e. the surfaces are not being pulled apart).

Not glue, necessarily. The coefficient of friction is not about surface adhesion. It is kinetic; glue is an additional static component.