A thought I've been toying with for the past few months . . .
As mentioned previously, the first war between the Cardassian Union and the UFP appears to have occurred from 2358-2362.
Consider the first couple of seasons of TNG (which starts in 2364) . . . the crew simply does not appear to be a war-hardened force. If anything, they act more like space hippies then quasi-military officers . . . Riker believing combat training to be a "minor province" in the make-up of a starship captain, Picard avoiding holding actual wargames, and so on. There are several examples wherein the idea of 'a generally-peaceful aim' would be a bit of an understatement. This isn't a bad thing in a time which can support it, mind you, but it was almost as if there was a cultivated naivete at times. Certainly it was a much different era than Kirk's TOS.
I think there is a relationship between that era and the Cardassian conflict. From Mosaic, we know that as of 2351 there hadn't been a war or other significant conflict for decades . . . the word "war" was hoped obsolete.
We also know of the Talarian border skirmishes (where the Talarians, near Cardassian space, are a remarkably low-tech people), the Tzenkethi war (apparently of the early 2360's), and so on.
Also, as noted on the Setlik III page in the Tech Archives, the first known use of the TNG pajamas was sometime between 2349 and 2354.
(And you never know . . . there might be a relationship there, too. The militaristic uniforms of the latter-TMP era, worn throughout the first half of the 2300's, might've helped cause some other races to blink faster than they would if the Federation showed up in one-piece speedo pajamas.)
If war was thought obsolete and evidence of unenlightenment . . . if the Federation hadn't been tested in real war for decades . . . if they showed up in pajamas . . . if they seemed to blink out of a spirit of conciliatory friendliness . . . if Earth was a paradise and the rest of the Federation seemed to be following suit quite nicely, with troubles minor . . . then the Federation's adversaries might've taken these things as a sign of weakness. "They are unprepared."
(Certainly if some backwards fartcatchers like the Talarians start rattling sabers with you, you know that you're not projecting anything resembling fear, nor are you absorbing such a society as a member anytime soon.)
In short, I would argue that the first half of the 24th Century saw a steady decline in the rather more martial philosophies of the mid-to-late 23rd Century. Those more martial philosophies were borne of the cold war with the Klingons at the time.
(Indeed, I think the Klingons are why the remarkably TNG-esque Earth Starfleet of the early 2150's were able to become the mid-23rd Century Federation Starfleet. Sure, the Romulans brought everyone together in war, but it was the decades-long cold war with the Klingons that really kept the Federation on its toes.)
After Organia and the eventual peace with the Klingons beginning in the 2290's, there just wasn't the same impetus anymore, and by the early-to-mid-2300's the hippyism had begun. To be sure, we know that during the 2340's the Federation got worried about the Cardassians, but worry is not a direct lead-in to a return to martial philosophies.
It's possible that no one recognized that three separate "western" powers challenged the Federation at the same time for the same reasons . . . this may simply have been viewed as a necessary 'taming of the west'.
In short, the Federation became complacent, and despite a brief spat of trouble with a few rabble-rousers in the west, they really never had much cause to question their complacency.
With the end of the western conflicts of the 2350's and early 2360's, then, it was a new dawning of the Age of Aquarius . . . harmony and understanding, sympathy and trust abounding, no more false or dark derisions, and so on. After all, the west was tame and they'd all soon see the light, the Romulans were being quiet, and by damn even the Klingons are friends! The only real worry was the Ferengi, but even they turned out to be a non-threat.
In other words, the early 2360's resembled the late 1960's in the United States. Sure, there were still hardasses around, but even the hardasses were pleased that the trials of the 2350's were over and might've secretly hoped that all would be well for a long long while.
Of course, as we now know, the idea was wrong. The return of the Romulans in late 2364 got a few balls rolling, but it was the "kick in our complacency" that the Borg produced (thanks Q) which resulted in a scare real enough that the non-warship-building Federation came out with the Defiant Class.
(Had the Federation encountered the wormhole and the Dominion circa 2364, I don't think they would've had the spirit to win.)
In any case, that's the general gist of my idea as to why there's such a gap between the attitudes in early TNG versus late-TNG / DS9. The ideals are still there, but there's a more realistic approach that, while perhaps not working as well at times, has certain merits.
Of further interest would be the period around 2380 or so, with the end of the devastating Dominion War. I can't help but wonder how the Federation's attitude would be circa 2400.