If one expects price to drop, selling a covered call is a poor way to protect one's shares. Even if one used ITM options, as share price fell, the delta of the call would decrease and the amount of hedge per point of drop in the underlying would decrease. IOW, the more the stock dropped, the faster your losses would accrue until they approach 1 to 1.
Your premise addresses when one would not want to sell a covered call. However, there are reasons to sell them. Less commonly, one owns shares that have risen and has a somewhat higher target price. Selling a CC at a nearby strike price will generate some premium income while waiting.
What your question ignores is that covered call writing is implemented when one has a neutral to mildly bullish outlook for the stock. While it does provide some modest downside protection, it's primary objective is increased income through stock ownership. The position will outperform the stock if share price drops, goes nowhere or rises a little. A large upside move will be an opportunity loss since you will not participate above the strike price. Writing covered calls will lower the volatility of the portfolio.
Covered calls and their synthetically equivalent short put have asymmetric risk (limited upside with most of the downside risk). An old saying about them is that "Most of the time you eat like a bird and sometimes, you sh*t like an elephant." In good years, you'll lag the market. In bad years, you'll lose but you'll outperform the buy and holder.
Now that I've told you the bad news (g), it's really not that bad. As per CBOE stats:
The CBOE's BXM index represents the returns of a monthly buy-write strategy where the S&P 500 is bought and one at-the-money call is written. Over the past 30 years, the S&P 500 has returned an annual rate of 9.9% with a standard deviation of 15.3%. The BXM has returned 8.9% with a standard deviation of 10.9%
The CBOE's BXMD index represents the returns of a monthly buy-write strategy where the S&P 500 is bought and one call 30% out-of-the-money is written. Over the 30 past years, the S&P 500 has returned an annual rate of 9.9% with a standard deviation of 15.3%. The BXMD has returned 10.7% with a standard deviation of 13.2%
If you have some sort of superior timing and selection skills, you shouldn't monkey with covered calls and short puts. Because of their asymmetric R/R, my preferential strategy for income is vertical and diagonal spreads where there is a floor of protection and unexpected surprises don't hammer me.