Combining the Woocommerce Login & Registration Form

Question

I am working with a client who is very insistent about his customer experience. He wants to streamline the Woocommerce login and registration forms. Most traditional ecommerce sites do have what seems like a combined form, so I see his point. I haven't seen anything on the market that resembles this. Can this be done?

Dream Scenario #1:

2nd and probably more likely scenario