I have only come across SEPA as a means of making transfers between bank accounts. Can it be used for payments too (e.g. instead of a credit card)?

It is also single currency - Euro only, right? Swift is global.

Dealing with many currencies and laws (e.g. countries with capital controls) is very complex.

SEPA also works for SEK now, other EU currencies are in pipeline.

Swift is just a messaging standard and a message exchange network (distributed). SEPA is that, plus a settlement system (in a nutshell). That allows for speed and much more (instant payments, request to pay, pay by phone number, credit/debit transfers, etc).

You're bound to deal with currencies once you make any kind of transaction that originates in one currency and settles (finishes) in another.

Also, does it support micropayments?

Yes, min transfer 0.01 EUR

We also have Wero now, which unifies the mobile payment systems in belgium, France and Germany, with more to follow. Promises to be a unified mobile payment system across Europe within a couple of years.

Sadly no one I've mentioned Wero to knows about it so I've never used it. I feel like banks were too set in their old ways and PayPal ate their lunch.

SEPA payments are quite expensive though, which most likely explains the prevalence of local payment system in every country.

The transaction cost compared to most domestic systems is absurdly high.