It seems to me that the initial popularity of "REST" was largely because it wasn't SOAP (and didn't have to be XML), but it was still a name you could give what you were doing that made it sound like you were following some sort of standard.
It's not hard, but I see very few differences between them. SOAP is easier to read/edit, JSON has less overhead/data, and REST...well, nobody could decide what REST was, so they just made it up or ignored it.
Just curious, what programming language(s) did you use to provide and/or consume SOAP APIs?
Perhaps my own experience trying to use SOAP can shed some light on why REST prevailed. In 2004, I tried to use the PayPal mass payment API from a Python application (in the now-defunct Quixote web framework). As I recall, I found one Python SOAP client library, but for some reason, I couldn't use it to access the PayPal API. It was all just so complicated. In desperation, I ended up writing a small service (micro-service?) to access the PayPal API using the official PayPal Java SDK. That service used Jython, because I just couldn't stand Java's verbosity. The main application communicated with the service using XML-RPC.
Compared to SOAP, when I discovered REST, it seemed refreshingly simple, built for the Web rather than awkwardly abusing HTTP as a transport for an over-complicated RPC protocol.