Television & Movies

In Shakespearean times, men played women and vice versa.

You're mistaken here. In Shakespeare's time, all actors were male. Female roles were played by pre-pubescent boys. A woman acting on stage was considered as shameful as being a prostitute.

Anyway, what really gets me on the size thing is that this could have been easily fixed! They routinely change the heights of both male and female actors in movies, making them shorter or taller as necessary by the script. It's trivial to do so using costuming and camera tricks. There is zero reason they couldn't have just made Elliot Page bigger. They do it for short cis male actors all the damn time.