They're not mutually exclusive. For best results, you should invest in an index fund and sell covered calls on it every month. Also, there's no "risk" created from a covered call. That's the 'covered' part. There is the possibility that you could "miss out" on an up move, but the trade off is the certainty that you will collect premium every month.

This is something that can be tested, and has been studied, and I encourage you to do that instead of relying on your bias here. Clearly you have some knowledge of the subject so sharpening on the finer points could be informative for you.