Arthur Miller, himself, stated that The Crucible was not a history. That being said, he did conduct a lot of research to write the play and create the characters given the play was based upon historical happenings.
The main reason why Miller would have struggled with creating characters for the play was the fact that the play was written in 1953. This was 261 years after the actual witch trials took place (the Salem With Trials took place in 1692.) Therefore, Miller did not witness the trials; instead, he wrote the play based upon the historical documents and references he found.
The second reason why Miller struggled with his characters in the play is one which is universal. Almost all writers struggle with creating characters. This is a normal process for writers. Writers must decide how much information to provide readers with, when to provide the information, and how to provide the information (through direct characterizations or indirect characterizations, dialogue, personal thoughts, and reactions of other characters).