There is a lot to like about this paper..
I had heard the story about Einstein's vacillation, and his ire at the rejection of his GW paper with Rosen - at a GR21 plenary lecture - but this is a great intro for those who did not have that privilege. There is indeed a lot we can learn about or test in theories of gravity, by studying gravitational waves. I too am an advocate that we need to have GW instruments with sufficient sensitivity and bandwidth to discern which cosmological theories work. I got to talk a little with, and Andy Beckwith talked quite extensively with, Paul Steinhardt regarding primordial gravity waves - and how current detectors are not nearly good enough.
But Strominger's talk at GR21 focused on how even the meager observations to date allow us to constrain our choices of alternative gravity theories. I am somewhat undecided about whether GR, extended relativity theories, modified gravity, or quantum gravity, yields the correct answer. My intuition tells me that strict general relativists try to carry things a bit too far, and end up with unphysical assumptions and false predictions, so there has to be some modification to make gravity work as we see it in nature. Have you seen the recent papers talking about an echo in BH merger GWs? This is supposed to be a signal for quantum gravity, according to the authors. What do you think?
I have to agree with George Ellis's comment above, that the subject matter is somewhat off topic. But I think, especially after seeing Nathan's comments, that a slight change in the narrative could have brought the subject back into focus. For example; talking about how even Einstein the founder's mind and opinion wandered about the reality of GWs could have made that section work like a charm, to deliver a message of how the wandering led to a goal. But the linkage failed to appear within the body of your paper, so I can only give partial credit for that, in what is otherwise an excellent paper.
All the Best,
Jonathan