It seems like information such as jr or sr would be helpful in family history research. I'd love to know why, when indexing is done, that they don't want that detailed added.
Its my opinion that they we dont include it because its a Name Suffix. These are things like Jr., Sr., I, II, III and so on. They arent technically part of their name, so they get left out. Its the same reason I believe we dont include Name Prefixes either. Those are things like, Mr., Mrs., Ms., Sir., and others like that.
I can understand that knowing whether its a Jr. or Sr. would be helpful in finding family members but I dont think we need to worry about that. Every piece we index with that person becomes that individuals source info so people searching would be able to tell them apart usually by dates. And, even if they cant, they can check the indexed file the info was pulled from and then can see on there the Jr., or Sr., that was originally on the document.
I hope this can answer some of your questions :)
The Researchers will get to see those details (prefixes, suffixes, terms, titles) when they are drawn to the image by your basic indexing. Nonetheless, some projects do make room for that information, and when required or requested and available, we index those fields.