Benchmarks for Functor Overhead

We are interested in obtaining and documenting benchmark results to determine the overhead of using functors with GAT expressions versus just directly using the Julia libraries referenced in instances.
This problem is related to issue #125, inasmuch as we would like to show that using the "backend agnostic representations of linear operators" is just as efficient as directly using LinearOperators or LinearMaps (has trivial overhead).
The relevant questions are:
Is there interest in this benchmarking being implemented generally (for more than just instances of GLA)?
What are some representative functions that would be useful to benchmark for speed and memory?