So I know it would reduce the "purity" of blind pick, but..
What if blind pick revealed the enemy team during the "choose your load out" phase? It still wouldn't allow for counterpicks, but it would allow you to for example opt into mirror shield if you're Udyr top laning against Teemo, instead of being stuck guessing what you're up against and kinda rolling the dice with runes.
I think it would be a nice mid-point between just playing what you want without thinking about counterpicks, and having the flexibility to reduce the pain in bad matchups (or increase the pain in favorable matchups, if that's your jam).
Thoughts?