As a user, you get your order confirmation and while it might take a bit longer for the money to arriveSetting up Direct Debits, at least the UK version, it's not "a bit longer" for your money to arrive, it's confirmation several days later vs. within seconds.
For ongoing payments like subscriptions this probably isn't a huge deal, but for one-off payments it makes less sense.
I much prefer debit, as it makes it much easier for me to get my money back if the seller doesn't deliver.
Unfortunately from the seller's point of view, that also means it's much easier for someone to claim to be a customer, get hold of your e-book/music/software/whatever, and then reverse the payment. There are procedures for disputing chargebacks on credit cards, but with Direct Debit the guarantee is basically that banks will reverse first and ask questions later, and the time limits for doing so are much longer (if there are any at all).
Again, this is less of a problem for ongoing payments for utility bills or something like SaaS where you can just cut off access if they stop paying, but for things like one-time downloads it's a huge risk for the merchant.