Starfleet does start to make that shift in the later part of the Dominion War with the Defiant and then the Akira and Alita classes, but the introduction of dedicated Federation warships also gets mixed up in the darker shift that the Picard show brings to the timeline.

But I don't think having ships which are both warships and science/exploration vessels and even having civilians aboard is not necessarily a bad thing. Starfleet ships are frequently expected to operate independently far beyond the reaches of Federation space for extended periods of time. That's the whole premise of the Five Year Mission. They can't rely on the Federation's reputation when meeting new life and new civilization and can't expect backup or rescue when going where no human has ever gone before. That does pretty much necessitate the exploration ships be armed. And the sheer length of the missions does make the crew bringing their families along a perfectly reasonable thing for the pampered postscarcity Federation crews to want.