As long as you have the appropriate levels of option approval then there's no reason why you can't do this (if the stock cooperates).
Covered calls and short puts are synthetically equivalent which means that they have similar risk and reward. The risk with either approach is that AAPL drops a lot.
If you pay commissions, by rolling the initial short put out if it looks like you are going to be assigned, you might incur fewer transactions.
Rolling out avoids have to buy the stock and that might enable you to collect some interest on your free cash if you brokers pays it interest on cash balances
If you intend to stay the course, trade time for avoiding intrinsic value. For example, with AAPL at $261.74, you sell the 12/20 $260 put for $4.00. One week from now, AAPL is $260 and the put is $3.70. Roll the short $260 put down to $257.50 for a small credit (5 to 10 cents?). Now you have $2.50 more of downside wiggle room and you still have the same potential profit. Plus, you will acquire the stock at a lower price if assigned. If you did not do this and AAPL kept dropping, you'd be giving up some of your potential profit from the $4.00 credit received.
Here's the big risk. If AAPL drops sharply, you'd have a large paper loss and you might not be able to write a covered call without either locking in a loss or having to sell a covered call further out in time.
Covered calls and short puts have an asymmetric risk/reward. That means that you bear most of the risk while enjoying only a small potential profit. For that reason, I believe that the only reason to do these is:
It's a stock that you're willing to hold but you have a target exit price. Sell an OTM call at your target price. Collect premium while waiting for your desired sale price.
It's a stock that you want to acquire at a lower price so sell the short put and collect premium until either you acquire your stock or share price moves up beyond your comfort zone and you move on to greener pastures
If you're going to chase premium just for the sake of premium, consider vertical spreads which level out the imbalanced R/R ratio of these strategies.