This is a behavior I myself have, and it often boils down to not wanting to use consumable items until my class features -- daily, short rest, or whatever -- have been burned. I hate to use something non-recoverable before something that is recoverable, and even then I feel like it's a waste of the item if the battle ends right after I use it and it didn't have a significant impact. (That is, even if my spell scroll contributed to the battle, if it wasn't an earth-shaking change to the fight, I'm left feeling like maybe I should've just used a cantrip instead.)
In addition, there's often a sense that the action cost is too high, for some items. A potion of healing that recovers less than the damage I took in a single round of enemy attacks doesn't feel like I'm making a good choice. I'm likely to try to push through even with 2 HP left, because spending an action to get myself up to 9 HP feels silly if the enemy is dealing 8 to 12 damage per hit. With or without the potion, I'm just as unconscious either way, and attacking instead might just end things here and now. And after the fight, do I really want to heal with a potion? I'm pretty beat up and we're out of healing spells, so we could find a way to sleep for the night instead...
This tends to get worse over time, as well. The longer you hold an item, the less useful it is, as the opportunity cost of using that item becomes higher. As the player character levels up, the consumable items you got several levels ago become weak compared to your improved innate powers. You're even more likely to say, "Why should I waste an action on this?!"
So how can you deal with this? I can think of a few potential options.
Give out fewer consumable items, but choose stronger ones.
If the issue is feeling that consumables aren't worth spending unless they have a big impact, play into that. Instead of giving the players four potions of healing, give them one potion of greater healing that really can take somebody from near-dead to full HP (adjust which potions I'm talking about to fit your party's level, of course). Instead of handing out a selection of below-level spell scrolls, let them find a scroll for a single spell that's a level or two higher than the players, something they need an ability check to cast. It's a risk, but if it works you turn the tide in a serious way.
If the players' hesitation is indeed based on the "save it for a rainy day" effect, then this could have the unintended effect of making the players even more hesitant to use their sweet item; but on the other hand, the fact that the effect isn't that great can be a big part of it never being "the right time" to use the item.
Put a time limit on the items.
I really like the idea of, say, healing potions that are only good for a few days before they go bad. As you said, it wouldn't make a lot of sense as treasure in a dungeon, but as something a local apothecary whipped up in thanks for the party's actions, it would be a great fit.
It wouldn't be a permanent thing, but you could place an adventure in an area with a pervasive aura of rot or a drained-magic area where non-permanent items start to degrade the longer you stay, so the items have to be used or lost. This could help get the party into the mind-set of using up their stored items, at least.
Remind the players.
Sometimes it's not that you really are thinking, "Oh yes, my feather token could help here -- nah, better not." Sometimes it's just that you forget the item list on your character sheet when you're in the middle of combat. You're deep in "What would a Cleric do here?" mode and don't really consider that second sheet that's off to the side of your spell list. If called on it later, you might come up with an excuse like, "Well, it wasn't the right time" rather than admit that you just forgot you had the dang thing. So sometimes maybe it'd be helpful as DM to just say, "Hey, remember you have an item that would be perfect here."
Provide NPC companions who can use the items.
If the problem is less "saving for a rainy day" and more "action economy and underwhelming effect", an NPC companion who doesn't have other options at hand might be a good way to burn off those items. An apprentice spellcaster who only has level 1 spells, but can use a scroll, wave a token, or feed potions to unconscious party members can be a good way to get use out of those items without forcing the player characters to actively use them.
Let them sell the items.
In some cases there's just nothing you can do. Like your stack of 48 hi-potions in Final Fantasy, sometimes you just have items you will never get around to using, and that's just the way it is. It's not my favorite thing, but at some point, maybe you just need to give the players a way to convert their loads of consumables into something less consumable that might actually make them excited.
Allowing them a way to convert a whole bag full of stuff they don't care for into a single wand of web or something may not be a bad idea; charged items often fix a lot of the problems I discussed, because charges feel a lot more like "use it or lose it" and are now more renewable than, or at least as renewable as, daily character resources. If you do this, I suggest limiting their options, and picking out items to offer that have more than merely combat use, which can help break out of that 'action economy' problem.
Another option is gifting those items to NPCs. Instead of selling them for gold or in exchange for other items at the Fantasy Swap Shop, handing over "weak" items to a local noble or organization might earn them boons and good-will that money might not be able to match. A bag of trinkets that the party doesn't really want could be a huge benefit to an army or constabulary, and might earn them favors, letters of introduction, or anything a bribe could do.