First of all, we had lots of issues with Direct Debit. And it takes a good few days (1-2 weeks) until things authorize. In the meanwhile, you have to provide free service in the hopes that it does.
Second, we had a potential gap with the equivalent of chargebacks. A customer could contact us for a refund, and we issued it. Then their bank (or them?) blocked the payment, which results in another refund + chargeback fees. So we can actually lose money...
Third, and take this with a grain of salt, because it could be specific to our audience, but we actually A/B tested it, and with/without Direct Debit option, our revenue was more or less the same. Some complained, but lots accepted using Paypal / CC.
We're still relatively small, so perhaps your comment applies and we're simply not big enough, but I'm really unsure how much of a big win this is. YMMV.
It's only really good for subscriptions rather than one off payments though. Not knowing if the payment was successful for 5 days is probably the biggest downside. Very low fees and low churn is the upside.
In this situation direct debit gives the vendor the comfort of delivering goods without payment, and it gives the customer the flexibility of ordering without having to go through a purchasing process.
Different from a debit card which is a debit from an expiring card.