What? If you write a put option, and it is executed, then you have to buy the stock for its strike price, which will be above its market price (that's why the put was executed in the first place). You end up buying the stock at a premium, not at a discount.
Here's a concrete example. A stock is trading at $100 and you write a put on it struck at $90, earning a premium of (say) $5. Then the stock falls to $80 and the put is executed, so you buy the stock for $90.
You now have something worth $80 and a $5 premium, but you paid $90, so you are $5 out of pocket.
Now you write a covered call on the stock struck at $100, earning a $3 premium (because it's further out of the money the the put you wrote earlier). The stock goes to $110, so you sell it to the call owner for $100. That's nice, you've earned the $3 premium and you sold the stock for $10 more than you bought it for (a total of $13 up). But if you hadn't written the call, you could have sold the stock for $110, and been $20 up instead.
If you also buy a protective put (say for $1) then that's an additional loss you bear in this scenario, since you can't execute the put.
If you're writing options, you're basically betting against market volatility. You'll do alright in the short term, but you'll get absolutely creamed if there's a stock market crash or other crisis.
For clarification you write puts at or out of the money. If executed, the premium earnt offsets the difference between strike price and spot price. No one is saying this guarantees against a market crashes but it acts as a cushion. You are still trading when you decide not to place a trade.
To put it another way, you make money when you buy, not when you sell. Therefore your purchase price is a margin of safety if done right. I carefully select the companies I trade by building up a 'conservative' price target based on a company's tangible book value per share (TBVPS). I try to write puts that offer a good risk/reward profile relative to the TBVPS. Even if I was caught in a market crash I'm as close to book value as I can get. Having done my homework I'm sure this company will outlast the extreme market sentiment. When such events occur I add to my position on the strength of my fundamental analysis. The market always overshoots and creates a wealth transfer opportunity.
In both my examples, the options were written out of the money. That means the premium is small (because the option is unlikely to be executed - premium is always largest for at the money options). Whether or not the premium offsets the difference between strike and spot totally depends on the size of the move! If the option starts $10 out of the money with a $5 premium, and it ends up $10 in the money, you've lost $5 whichever way you look at it.
Your advice of combining options and stocks is at best a little naive, and at worst will be a disaster for anyone who's not a sophisticated options trader.
Here's a concrete example. A stock is trading at $100 and you write a put on it struck at $90, earning a premium of (say) $5. Then the stock falls to $80 and the put is executed, so you buy the stock for $90.
You now have something worth $80 and a $5 premium, but you paid $90, so you are $5 out of pocket.
Now you write a covered call on the stock struck at $100, earning a $3 premium (because it's further out of the money the the put you wrote earlier). The stock goes to $110, so you sell it to the call owner for $100. That's nice, you've earned the $3 premium and you sold the stock for $10 more than you bought it for (a total of $13 up). But if you hadn't written the call, you could have sold the stock for $110, and been $20 up instead.
If you also buy a protective put (say for $1) then that's an additional loss you bear in this scenario, since you can't execute the put.
If you're writing options, you're basically betting against market volatility. You'll do alright in the short term, but you'll get absolutely creamed if there's a stock market crash or other crisis.