But yet these abominations from the 80s which fit terribly with Internet are still here thanks to the oligopoly in financial industry.
Security
Debit/Credit cards have poorest security among all available payment methods. One can steal your funds simply by memorizes information written on your card or by taking a photo of it.
Safety
How can you call a payment method reliable, when any company to whom you ever given your card details can charge it at any time without your consent or knowledge?
Recurring payments
Recurring payments are solely created as a loophole for merchant to legally scam you out of money. For every month until your card expires.
Charge backs
A way for cardholder to get payback with merchants.
Totally not suitable for online payments
Why do you need a physical card when you make non-physical transactions?
Expiry date
What is the point to to replace your card with similar one every 3–4 years, especially when most of the time no new features are added?
Slow process of replacing your card
When ever your card gets lost, stolen or hijacked by fraudulent merchant you need to replace it and wait for few weeks until you get new one.
Troubles with online payments
Most of the merchants are so afraid of card scams that they will not allow you to pay online with virtual card or with card that is registered in different country than where you are currently located, which makes cards absolutely useless online.
Transaction limits
Even if you have lot of money on your account, the card will still have transaction limits of only few thousands $/€/£ per purchase and per day.
Can’t block merchant
There is absolutely no way to block fraudulent merchant if he keeps charging your card. The only way is to dispute all his transactions (and wait for few months) or to block your card and wait for a couple weeks to get new one.