I think there's a lot of stigma with people only trusting "new" stuff and anything "old" is automatically inferior in some way. IMO age is only a number. If you can't tell WHY something is no good (composition or potency breaks down? New research has taught something is actually ineffective or dangerous?), it should still be good. Our company is a blend of new and old, so it's expected that not everything is going to be fresh off the truck. We have some ammonia packs in the medical kits to wake up a fainter that have NEVER been used. One cabinet might be 30 years old, but those ammonia packs are still sealed so they're still in there.
Ammonia packs might still be good, but adhesives break down, elastomers can slowly outgas and dry out, and of course certain kinds of drugs may lose potency.
That means old bandages won't stick as well, dressings may not be as pliable, sterile packaging can't be guaranteed to be sterile anymore, etc. There is rarely such a thing as "sealed." Pretty much every material you handle is gas-permeable to various degrees. It takes a long time, but it's a real effect.
You can test some of this yourself, but some you can't test. Most of the time it's fine. Chances that your non-sterile packaging will give someone a serious infection are slim. A bandage falling off isn't the end of the world. Expiration dates based on empirical testing are going to be for the worst-case (but still acceptable) scenario the manufacturer expects the product to see, and likely based on when these negative effects
start to occur. Plus a considerable safety margin. Meaning things will last a lot longer in your 24/7 climate controlled 72 degree shop than in the back of your car.
Most companies though would rather spend the $100-$200 replacing the kit every few years than start digging down into the minutiae. Not to mention the liability risk. It's a lot easier to say "everything in this new pack is guaranteed to be in good condition and work as intended until XX-XX-XXXX" than to say "oh sure it's like 20 years old or whatever but does that
really matter I mean yeah those aspirin look a little brown and half the bandage wrappers have come undone but they still work fine I bet."
Airplane maintenance also involves scrapping perfectly good parts to replace with new ones that have guaranteed performance for X hours. Not the same stakes in this case of course, but a similar principle applies. And don't forget that the quirk of piece-meal replacing stuff that gets used but never checking expiration dates, is that the most rarely-used stuff is also going to be the oldest. If you're lucky it won't be something life-critical that fails you in that 1-in-20-years accident because it was never replaced.