The one place where maybe they have some utility even in the above scenario is for the locked-but-partially-broken doors. Since those are part of the One True Path through the POI, it might be worth it trying to pick them instead of bashing them open, so as not to wake the former residents.
Don't think you can lockpick doors (which is odd).
Basically lockpicking has a couple of issues:
1. It has no clear advantage over simply bashing a container open
2. Miner 69'er makes opening safes quicker and generally makes mining quicker too, it has multiple uses so the points are better invested
3. The perk itself doesn't have enough of a bonus
Possible solution:
Make the perk and lockpicking have more bonuses and applications. Give lockpicks a passive bonus and have three tiers of lockpick.
Lockpick Tiers & Passive:
Simple Lockpicks: +20% Unlock Loot
Iron Lockpicks: +40% Unlock Loot
Steel Lockpicks: +60% Unlock Loot
Unlock Loot = Bonus loot obtained when unlocking a container rather than bashing it open.
Perk:
Level 1: Pick locks 33% faster. You can unlock wooden doors. +20% Unlock Loot. 25% chance lockpick doesn't break on fail.
Level 2: Pick locks 66% faster. You can unlock metal doors. +40% Unlock Loot. 50% chance lockpick doesn't break on fail.
Level 3: Pick locks twice as fast. You can unlock all doors. +60% Unlock Loot. 75% chance lockpick doesn't break on fail.
The Benefits
1. Now, even without skill, lockpicks are worth trying as they have a chance of better loot.
2. The perk offers the unique content of getting through doors more easily and stealthily.
3. The perk adds a distinctive loot bonus in itself, compounding the lockpick bonus to eventually more than double container loot.
4. A chance for a lockpick not to break is better than a chance of not failing. No one can see when they succeed a check, but it's easy to notice when a fail doesn't consume a lockpick. This is better feedback for the player.
This basically means that bashing into a container is better as an option when you simply have no lockpicks left. Timed Charges should probably have their own Unlock Loot bonus. The candy could potentially double the Unlock Bonus for a few minutes.
This essentially makes lockpicking a good early game loot bonus, amplified by the perk. With the long term benefit of door unlocks.