Ehhh, no? Our debit cards are used for in-store payments, and literally every single bank allows you to use them for online payments too. We just developed systems which don't depend on handing random people a bunch of "secret" numbers and hoping they don't defraud you.

For example, in The Netherlands *everyone* uses iDeal. Basically, the store does a 302 redirect on checkout to your bank, sending along the money owed and the destination account. The bank authenticates the user, confirms that they indeed want to pay it, and redirects back to the store. It... just works!