There are a lot of very legitimate reasons a person wouldn't want to talk about (i.e., "dredge up" or "hang onto") the past. Keeping some conversation limits in a new relationship is something a lot of people think it's the best way to give a new relationship time to develop - or fizzle out, in which case, a lot of "deep" talk that was wasted on a non-friend is avoided. Too many people, maybe, tend to share too much way too soon (and it can color the relationship).
I think I'd be more concerned if the past wasn't the only thing the person wouldn't share. Not that I meet all that many new friends these days, but what I tend to notice is whether someone seems to have some version of "roots"/connections to other people, or even pets. It would depend on the age of the person and the relationship, but if I thought I might end up being close friends with someone I'd probably notice whether they seemed like they had those connections to important people in their life. If it was an elderly widower/widow with no family left that would be one thing. I'd be a little more concerned with someone younger who didn't want to talk about the past and never talked about/or spent time with people s/he was close to.
As for the no-talking-about-the-past thing (but having families and/or friends, etc.), I don't see that as a big deal. A lot of people just think it's healthiest to keep the past in the past, unless/until there's reason to talk more about it.