[Tarq0n]

No, debit cards in most of the world do not function for remote transactions, even if they have a Mastercard or visa logo. My bank's cards for instance are Mastercard's "Maestro" product which is in-person and debit only, and has alternative infrastructure for online payments.

[napier]

Which parts of the world are these? I’ve used debit cards issued by various European and US banks for online payments all over the world since the ‘90s.

[kqr]

What part of the world is "most of" it in this case? Where I live, Maestro and the like are considered children's cards for the reasons you mention, and real debit cards work just fine for online transactions.