Covered calls question

So I was thinking something about covered calls. Let's assume You sell a covered call on Amzn 2 or 3 weeks out with a strike thats like $2 above current price. Your only risk is that Amzn will go above that and you will miss out on a value for selling it.

However, to counter this risk, what if we use exactly all the premium money we got to buy Amzn call with the same date but strike that is just under the current Amzn price.

This way we get a “free” call option without any risk. Either Amzn stays lower or the same price in which case we gain nothing and lose nothing since we keep the premium but that premium is gone since we invested it in a call. Or the Amzn actually goes up, and we make more money on the call option than we actually lost on Amzn going up and messing with our covered call.

Am I missing anything here? Is this a good strategy?