A responsible broker will not just give anyone level 4 authorization on a whim from answering a few questions. They will only if they see the customer has had experience responsibly trading options for some time and demonstrate some level of risk management when managing their portfolio. You can quickly blow out your account with naked calls. Imagine those with OTM naked calls on PAR or MFE.
I'm surprised no one has challenged this assumption. Can you give some evidence that price action is random, controlling for different time frames?
You can lose a lot of money selling naked puts too. You would have lost a lot of money shorting PAR or MFE, yet most brokers will let you short stocks. It's always possible to blow out your account. Certainly no one is suggesting selling calls on likely takeover targets.
Selling naked options isn't a good idea, period. The whole point of options is to define the risk ahead of time. Selling naked is completely against that. It's like playing Russian roulette.
If you have decided that you are willing to buy 100 shares of a stock at $30 it is no more risky to sell a $30 put than it is to use a limit order to buy. If you have decided to short 100 shares of a stock at $45 it is no more risky to sell a $45 call than it is to use a limit order to sell short.