I think what you mean is a "general practitioner" who doesn't specialize in one field but does what I would call "bread and butter work" where they might be asked to draw up a will, help a family through bankruptcy, represent a speeder in traffic court, handle a minor personal injury suit, etc. Otherwise, "family law" is a specialty that some attorneys practice exclusively. There are tons of attorneys doing both everywhere.
I have a friend that graduated just two years ago, struck out on his own as a GP, and then bought out a small, local firm that does family/divorce law and estate planning...and this was in a major legal market, not a small town
So yeah, it's definitely still a doable thing.
Also, from reading the boards on this site it would appear that if you don't jump into law school right away you are at a disadvantage from the get - thoughts?
I don't think this is true at all, especially if your goal is to set up your own practice relatively soon after law school. When you have to drum up your own clients, age lends you credibility. I have been told that it's more difficult for people who went to law school after working for 15+ years to break into BigLaw (allegedly because they want younger people who have more "energy" and fewer outside commitments), but that's not impossible either.