I think there are a number of misconceptions on this thread
1) I have been using my credit card online to pay for goods for at least 25 years. I have never had any worries about security paying that way and it has never been a source of fraud. The same applies to my DH and my children. Any fraud tht takes place will not arise from paying online, but who you are paying it to. Use known accredited retailers and there should be no problem.
If you think just typing a credit card number online puts you at greater risk than saying it over the phone, then you are, regrettably, misinformed. Whether saying the credit card number over the phone or typing it online. If the person the other end is out to defraud you than the risk is the same. If they are not you will not be.
2) You do not need to bank online to use a Debit card to pay for things. I regularly use my debit card online to pay for things, but I have only moved over to online banking in the last month.
3) You can open a bank account online. You do not need to travel to a bank branch to do so.
4) Two thirds of all credit ard holders clear their balance at the end of each month so that alone should not be reason to stop your card.
A more likely reason is that you do not use your card frequently enough or there is not a signifcant balance to pay at the end of each month. Every time you use your card to purchase something the credit card company charges the entity - person, or company - a commission fee of up to 5%, It may be that you are just not spending enough each month to for the bank to earn enough income to cover the cost of servicing your card.
Banks are not social services, why should they supply you with a card if they cannot recoup what it costs them from any charges you pay and suppliers pay?
Ons solution could be to only have one card between you, perhaps in your name, with your DH as a second card holder, so you both have the freedom of a credit card, but only one account
We are in our 80s and have never had any problems with our credit cards - and we clear the balance every month - and, like most people, always have done.