I think the initial premise of the series was one of exploration in an era where most conflict had been resolved, peace with the Klingons and all that.
I think it's akin to that era in the early nineties, just following the fall of the Berlin wall and the end of the Cold War, where like idiots, I and many people thought that we'd finally passed all that stupidity.
Then Yugoslavia fell apart, and then Rwanda, and then all the Al Qaeda nonsense and we realised that nothing had changed. I think TNG was basking in that sort of peaceful euphoria in its early seasons, and it made sense to develop a ship as a community rather than a military hierarchy. It would have also allowed potentially for more soap opera storylines should the writers have wished to focus on non-Starfleet members of the crew.
Obviously that's not how the show developed, but it's only after the retcon of a recent war with the Cardassians that the family starship idea started looking ill-considered.