ApexClassMembers aren't the same thing as ApexClasses. If you want to work with an ApexClassMember you will need to create it through the tooling api first.
//First, the MetadataContainer
JSONObject metadataContainerRequest = new JSONObject();
metadataContainerRequest.put("Name", "SaveClass" + id); // Any unique name
JSONObject metadataContainerResponse = ToolingApi.post("sobjects/MetadataContainer", metadataContainerRequest);
System.out.println("MetadataContainer id: "+ metadataContainerResponse.get("id"));
// Then create an ApexClassMember.
JSONObject apexClassMemberRequest = new JSONObject();
apexClassMemberRequest.put("ContentEntityId", id); //This is the salesforce ID of any existing ApexClass.
apexClassMemberRequest.put("Body", body); //if not changing the body can probably be excluded
JSONObject apexClassMemberResponse = ToolingApi.post("sobjects/ApexClassMember", apexClassMemberRequest);
System.out.println("ApexClassMember id: " + apexClassMemberResponse.get("id"));
//get the ApexClassMember you just created. Should include the SymbolTable.
JSONObject apexClassMemberResponse = ToolingApi.get("sobjects/ApexClassMember/" + apexClassMemberResponse.get("id"));
I assume this is for performance reasons because salesforce probably doesn't want to store and re-create the entire symboltable every time you save a class.
You could of course do this all through workbench as well but that is a bunch of JSON generation and it might be easier to just spin up something quickly in your language of choice.