It would probably be better if instead of nobody being able to see who you pick, you can manually select yourself whether you want people to:
1. nobody but myself can see my demigod
2. only my team can see my demigod so we can collaborate on strategies and not all have rooks
3. everyone can see my demigod
4. random demigod for me
5. everyone gets randomized demigods(there can be overlap with having multiple same demigods in the same team, but it's just a matter of probabilty)
Also, if you could, please post your ideas/features into the master threads I created with the template I provided. http://forums.demigodthegame.com/350733 Thank you!