This would be a very good feature for TB as it's a feature that other platforms have though Magento tends to have this provided as expensive extensions; this would be a draw to people away from them platforms if it was part of the core as it's a growing trend in 2017.
This has to be done in conjunction with the payment providers due to the issues with PCI DSS compliance and storing customer card data. Many of the large payment providers allow for integration whereby they store the customer data in secure tokens on their PCI compliant servers. Both WorldPay and SagePay provide this service and they cover the UK though I don't know about the rest of Europe.
You might want to take a look at AheadWorks Magento extension for this to get some ideas of how they do it.
Hello from 2020. I disagree, for example here https://store.belvg.com/ you can find free Magento extensions. So hurry up!
Recurring payments in thirty bees
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Hello from 2020. I disagree, for example here https://store.belvg.com/ you can find free Magento extensions. So hurry up!