The thing that gets people is the psychological bit - when you split a £60 purchase into four £15 payments, your brain doesn't register it the same way as handing over sixty quid at once. I've watched friends end up with three or four of these services running simultaneously, each with different payment dates, and suddenly they're juggling repayments they half-forgot about. It's easy to lose track of what you've actually committed to.
The real problem is that these are basically interest-free loans for stuff you don't need right now, which means you're spending money you haven't earned yet. If you've got solid income and you're only using it for something you were already planning to buy anyway - like replacing worn-out shoes or a piece of clothing you actually need - then fine, the maths works out. But if you're using it because it *feels* like free money, you're setting yourself up. One missed payment and you're dealing with late fees, and it tanks your credit score too.
The honest answer: if you have to ask yourself whether you can afford something, then splitting it into payments doesn't actually make you able to afford it. It just delays the problem. Stick to what you can pay for outright, and use these services only when you genuinely need to spread a cost you've already decided is necessary. Otherwise you'll end up like some people, paying off last month's impulse buys for the next three months.