"But why does the typical soldiers funeral differ so much the typical policeman's funeral?"

That's a good question and I'm not sure I know the answer. Others have touched on this as a time honored tradition and that's probably the best answer. I would agree that out brave soldiers deserve much more and do not get the recognition they deserve. As to your original question, I have attended many police funerals for officers I knew and worked with from local agencies and for some that I didn't know personally. In every instance, I went on my own coin and never even considered being reimbursed.