So, if you're unaware, the basic math of PF2e's armour items assumes that for light and medium armour, (item bonus + dex cap) = 5, and for heavy armour, = 6. This means that as long as you can pick an armour that has a lower dex cap than your dex bonus, you are expected to be getting either 5 or 6 AC from your armour.
With all that said, there are a ton of armours out there that offer some kind of tradeoff, where that formula doesn't hold. For example, the Armoured Coat gives +4 AC between item bonus and dex cap, but it has the flexible trait which negates the check penalty to athletics and acrobatics checks. In my mind, that's a crazy tradeoff to make. The extra AC is so much more important.
At the end of the day though, I don't have the time to analyze the tradeoff offered by all of these "sub-optimal" armours. So yeah, I'd love to hear if anyone has experience with an armour item that yields less than 5 AC (or 6 for heavy armour) and yet the tradeoff was actually worth it for them.
It's entirely campaign dependent. If you're in a campaign where the challenges are overwhelmingly PL-1 or greater enemies on standard flat, dry surfaces, there's no reason to play with niche gear.
But the rule books are big toolboxes, meant to provide the tools necessary to run any kind of campaign you want. One that involves hanging out on a lot of ledges? Squeezing through narrow passageways? Dealing with geographical Hazards during combat (note to self: run more combats on ice)? Fleeing from enemies regularly? Then yeah, having that extra DEX on your skill rolls might be more valuable to you.
Even then though, flexible only matters if you aren't meeting the strength requirement of your armour. So it's niche on top of niche. It's crazy to me that they even consider offering people the option of +1AC for flexible. It's a very weak trait. Something that at least offered some alternative damage mitigation, like say a small flat amount of resistance to energy damage, that might be worth sacrificing a point of AC. But I just don't see it for a trait which is likely doing nothing if you have even a little bit of strength.