This is now in the Function Repository!

The new version is named RuleNetGraph, and there have been several improvements:

1. You can use Subscript to name layers
2. Pure functions and functions supported by ElementwiseLayer and ThreadingLayer are automagically converted into valid Layers! (ElementwiseLayer taking precedence)
3. You can provide a list of rules as the input.

ResourceFunction["RuleNetGraph"][LinearLayer[64] -> LogisticSigmoid -> (#*17 + 8 &)]

The implementation is fairly similar aside from some changes to improve usability, but feel free to download the source notebook from the function repository site view the latest changes.

This is an interesting idea, thanks for suggestion, Alec. I encourage you to submit this to the Wolfram Function Repository (WFR) where it gets reviewed by internal teams. If the design will prove to be fault free and show usability, it might be considered for adoption into the built in architecture.