If I recall correctly, the Commordore did leave a will... and Jimmy ripped it up in the presence of Gillian and the Commodore's lawyer. This made him the heir (to the intestate Commodore) with his son, Tommy, the next in line. Zero for GIllian.
My clear impression was that Richard knew - before Jimmy went to the fatal meeting with Nucky - that it would mean Jimmy's death. Richard warned him that no matter how successfully Jimmy could right the wrongs (and he did!), Nucky could never forgive him. Jimmy agreed. Richard also knew that Jimmy gave Tommy his dog tags before going to meet Nucky and the import of that was not lost on Richard.And Jimmy declined Richard's offer to accompany him to the fatal meeting, indicating that he knew the outcome in advance.
Declaring Jimmy dead under the circumstances would entail Gillian waiting for a statutory length of time to pass - in most cases 7 years. She could not wait that long, so she needed the body.
What strikes me as evident now is that Gillian can no longer pretend to be Tommy's mother, which is something she seems to need.
Re: Bobby Cavanaugh, I totally agree. He's annoying and I can't wait for him to be gone.