Since its creation 3GPP SA5 has seen a couple of protocols already: CMIP GDMO, CORBA IDL and SOAP WSDL.
CMIP was specified by the ITU-T and geared towards the management of telecommunication networks. It was very powerful but suffered from the lack of tool and product support. CMIP was soon replaced by CORBA. CORBA was widely used in the IT industry and the telecom world hoped to overcome the CMIP issues with it. But CORBA became more complex over time, developers complained about expensive CORBA-ORBs and problems with firewalls since tunnelling through port 80 is not easily feasible. At the same time the World Wide Web and its technologies saw an impressive rise and CORBA became more and more a nice product. Soon developers hoped for the better by using the technologies of the World Wide Web, namely HTTP and XML and SOAP was born. SOAP is basically RPC where the operations are described with XML and HTTP POST is used as transport. In a way this was also a step backwards since CORBA and CMIP were object oriented approaches with operations being invoked on the objects and not against service endpoints. That CORBA was not used by SA5 in this way because so called facade objects (only real CORBA objects with IOR) were introduced as service endpoints for scalability reasons is another story.
As with CORBA, SOAP required extensive software support on the client and server. XML was soon considered complicated and running XML instance documents through parsers even more complicated. Developers started to love JSON and HTTP that is readily available on many servers and clients. In 2000 Roy Fielding published in "Architectural Styles and the Design of Network-based Software Architectures" with REST (REpresentational State Transfer) a new architectural style for designing interfaces with strict focus on resources and not operations. HTTP and JSON can be used for implementing REST. More and more developers adopted RESTful HTTP based interfaces. Today this is the predominant approach for APIs.