So writing covered calls means you are SHORT calls instead of LONG them like me, and that interest rate rise works in your favor, hastening the decline in the value of your covered calls that you are counting on to make you money.

It might be closer to a wash when you consider that, other things being equal, a 5% price rise to a covered call strike is more likely in a higher inflation world than in a lower inflation world.
Once you take out the cyclical squiggles, equity prices are roughly inflation adjusted on average.
Other things being equal, average equity prices rising at a nominal 6% in a 1% inflation environment will tend to rise at 10% in a 5% inflation environment.

Not true when inflation gets so high or so low that the economy breaks, but those situations are thankfully pretty rare.
And not necessarily true for specific individual firms, some of whom will be unusually sensitive (for good or ill) to inflation rates.
But for the average firm in the average year, earnings and prices tend to adjust for inflation trends.

Jim