More Random Drafting?

I was thinking about how games get set up, and started toying around with ideas to mix up picks by introducing a more random element.  No this isn't for anything serious, but more for a pick up game or things of that nature.

This is assuming a 3v3 matchup.

Start with a set of 15 cards, one corisponding to each hero and remove one at random and set it aside, face down.

Then deal face down 7 cards to each team.

Each team chooses 3 cards to keep and 1 card to ban. 

The baned cards are added to the removed card from earlier and the teams trade the 3 cards that where not chosen or banned.

Teams now chose from their six cards their heroes and place the chose cards face down and set aside the unchosen cards.

Once both teams have chosen, their choice are revealed.

Then, a coin flip determines who gets to choose first turn or Pick position.

For 2v2: Remove 3 cards at random at the start and deal each team 6 cards

For 4v4/5v5: Players do not get to ban a card from their 7 options.

Thoughts or other ideas for a more randomized draft?

This is pretty interesting.

For now I'm still focused on learning the characters and on thinking through how I would handle the way tournaments are doing drafts and bans, but if I ever get to a point where I'm just playing lots of skirmeshes w/out an eye on the tournaments, this would be a fun way to mix it up.

I would modify this by allowing the other team to ban one of your cards.  This prevents teams from simply taking their best three randoms.