So I tried this and think that one of the issues that stops people from sharing is that you don't really make it easy and inviting.

I tried the practice runs: Why is there no "share practice run results"?

I played a real game: Why can't I share results from the first run if I don't want to play further?

Finished 3 tries: The share results button has no feedback - I clicked it, why is there no "results are in your clipboard now" text? Why no platform specific buttons with a ready Tweet / fb post? (you can embed the contents of the message in the link)

What's stopping you? Why is the last game you shared on Twitter from March if you want to make it more popular?