This is passably useful. Essentially this means that anything you’ve picked once, you never have to pick again. The two really useful points for this are if you return to a dungeon after it automatically restocks itself, or if you return to the house of someone rich to rob them blind all over again when they replace their stuff. Really, though, you’d rather get more Lockpicking experience, so.... yeah.
Marginally useful, this makes somewhat difficult locks into easy locks. Nothing new to see here, move along.
Depending on your experiences playing Skyrim, this perk will either be hugely useful or mostly pointless. If you find yourself running out of cash a lot, you want this perk and you want it very badly. Adding up to 100 septims per chest to your treasure intake can have a huge impact on your ability to afford things, but only if you’re not the type of player that loots everything valuable from everywhere and hocks it as soon as you get back to town. Players who loot valuable gear constantly and sell it will probably not need the cash enough to care much about this- except for the perk that comes off of it.
The really big reason to invest in the Lockpicking perk tree, Treasure Hunter gives you something much more valuable than gold- a chance at game-changing gear or item finds. While it’s a thoroughly random effect, the perk can plant anything from a basically useless Iron Sword on up to a Dragonplate Cuirass into each chest depending somewhat on your level. It’s always a gamble (why do I want Imperial Boots when I’m wearing Glass or Ebony?) but when it pays off it can give you items you wouldn’t normally be able to get yet, or wouldn’t normally be able to get without making them yourself. That makes it actually worth more to characters who haven’t got Smithing in particular, or other crafting perks in general.