How to get a credit card when you don't have credit?

I have a problem. I am in my late 30s, but I don't have any credit cards and no one seems to be willing to issue me one.

I have a flawless credit history. When I was in my 20s I took out $30,000 in student loan debt, and paid it back fully and on time. In my late 20s, my credit was good enough to buy a new car without a cosigner, and get a good interest rate, and I again paid it back fully and on time.

However, I never had a credit card because I never needed one. I have tens of thousands in savings and never needed to borrow money for any purpose in my day to day life.

However, in the last couple of years I saw certain businesses that I engage with regularly that offer cash back or other benefits to having a card through them, and I thought this sounded good, so I applied to a few about a year apart of each other.

I get reliably turned down for cards with $200 credit limits 😂 I don't even want to borrow the money, I just want access to the discounts. As my credit history is 100% clean (I do check), it clearly must be the result of not having utilized credit in recent years.

Is there a way to fix this that doesn't involve taking out a card with outrageous terms? I don't care about interest rates, but I have no desire to pay someone actual money in terms of monthly fees and the like to just possess a low limit credit card.

Even my bank tried to convince me to take a low limit card without me asking, and then when I officially applied, they turned me down, and I have had accounts with them since I was 5 years old, and provided their staff with a paystub that they wanted to see (I have reasonable income, about $50K a year), and have always been in good standing.

I have no outstanding debts or liabilities or loans of any kind, so am I just out of luck at this point on getting those credit card perks?