There's always an order of actions, even if you don't realise it.
If A kills B and B kills C, does C die?
If a Kira tries to kill Kiyome, Mello tries to kill that Kira, and Kiyome tries to mob the Kira, what happens?
If a Kira kills Shidoh and Shidoh tries to take the notebook from that Kira, what happens?
If a Kira tries to kill Kiyome and Kiyome tries to mob Gelus (not Jealous), and Gelus tries to save Kiyome, what happens?
Depending on the interpretation of the order of actions, many different outcomes can be foreseen.
1. Kiyome mobs Gelus, so Gelus is unable to save Kiyome. So the Kira can kill Kiyome and Gelus is mobbed.
2. Gelus saves Kiyome and Gelus is mobbed for the next cycle.
3. The Kira kills Kiyome and Gelus is not mobbed.
All three of these can be justified by different orders of actions. Although the third one would be counter-intuitive. OOA is needed whenever there are 2 or more actions that affect other actions (Kira's kills, Kiyome's mob ability, and Gelus' saves according to some).
A published OOA lets the players know what to expect in these situations. Additionally, it allows for consistent posts from the host so the players can use logic to deduce who did what and how the situation in the night post was reached. If there are different results from the same actions every night, anyone can tell you that the game is too random. The OOA is the host's way of letting the players know how he compiles the actions.