Faking maturity on Facebook: underage accounts

What I've always wanted to know but been afraid to ask. So I'll risk general offense in the hope of getting some answers.

Why the fake account for your kid who is legally too young to be on Facebook? I know you know it's there, because s/he's in your friend list.

Why I haven't and I wish you wouldn't

1. It's fraudulent. Here's lesson 1 on "it's OK to fake your age to get in where you shouldn't;" what could possibly go wrong...?
2. It exposes your child randomly to inappropriate material, messages and ads. Facebook's only parental control setting is requiring your child to be 13 - why blow that?
3. It allows your child to send private messages to other Facebook users.
4. If I'm your friend on Facebook, your underage child will see our interactions and could potentially participate. Which could mean all THEIR underage friends might see it. Sorry, but ewww. My young adult nieces and my parents are in my network, and that cramps my style enough.

If you wouldn't invite your children to your pub crawl, why invite them illegally onto a worldwide social network?

Is 13 just forever to wait, when all of their friends already have one? 

Is it never too early to start putting yourself out there, counting how many friends and likes you get, with the added bonus of cyberbullying?

Are they growing up too slowly?

I'm only seeing the downside here - please supply some balance!