Compositional problems and motion problems are visible at low resolution. Type problems and texture problems are not. That split tells you exactly what a proxy pass is for and where it stops being useful.
The economics are simple: a proxy costs a fraction of a full render, so testing five compositions in proxy and rendering one at full quality is cheaper than rendering three at full quality and picking the least bad.
The failure mode is treating a proxy as an approval. A client who signs off a proxy has approved the composition, not the frame, and that distinction needs saying out loud before it is discovered at delivery.
What can a proxy render not tell you?
Anything about legible type, fine texture, or fine extremity detail. Those only appear at full resolution and they are where most failures live.
Should clients see proxy renders?
Often yes, for composition decisions, provided everybody understands they are approving the arrangement rather than the image.