A normal SEPA payment, is a "push" affair. These have (for all intents and purposes, though not technically) been a thing ever since the euro was introduced, whereas SEPA Direct Debit is more recent, replacing many of the existing domestic direct debit schemes.
Then there's the Instant Payments bit: these are a thing but they're not used all that often (yet?). Most banks charge a hefty fee for an instant payment (mine charges €1.25). Some banks don't offer them at all. Adoption will grow and costs will decrease over time.
In most countries, payments within the same bank have been instant (and free) for a very long time. This is one of the reasons why many companies have accounts with multiple banks.
I'm sure some "weaker" european countries may have laxer fraud controls, but that's a temporary problem. ECB reporting is quite strict, and most banks do take fraud detection very seriously. Reputation is important for a bank, and if you're a truly disreputable bank you'll soon find yourself without friendly correspondent banks. Then you'll have a choice: fix your fraud problems, or become a useless island.