The fact that SOAP is not reasonably supported in a browser was a huge reason it fell down. When SOAP first came on the scene, complicated AJAX based applications were not typical. But as more and more JSON/HTTP APIs emerged in conjunction with browsers becoming more powerful and rich apps build built in them, the meaninglessness & complexity of SOAP grew.

Also, another major issue with SOAP is that most all of the popular tools would generate classes based on a WSDL. This creates a toolchain issue that is readily solved for someone experienced, but can really suck if you are new to the idea of generated code working it's way into your project.

Much worse was the scenario of WSDL versioning in conjunction with these tools that generated classes. If the API never broke backwards compatibility, you should be OK and can just use the newer class representations, counting on the service and tools to deal with null fields appropriately (not always true unfortunately). But if version bumps of an API/WSDL broke backwards compatibility... then you had to have separate class hierarchies for different versions of the WSDL; what an intense headache. Contrast that to web REST APIs; without a formal schema and a lack of class-centric tooling, client libraries would often let the author stuff in the params themselves and let the serializer stuff in the body based on the params; so yes your API is not as formal, but this isn't a big issue but offers infinite flexibility in dealing with one-off versioning issues or interop issues.

As someone else mentioned, some platforms couldn't interop with others (differences as it related to simply stuff like nullable fields or primitives existed all over; total nightmare), and some features of WSDLs didn't translate well to certain languages.

A great WSDL author would know to make their WSDL as simple as possible, because they had spent time working with various language toolchains and new the limitations out there, but that's asking way too much and not realistic for someone to have to spend all their time trying to understand all the ways someone in language XYZ might use their WSDL.