I used to do lockpicking as a hobby. It's not as easy as it looks in the movies. However it can also be done really easily sometimes - depends on the lock. I can pop open most Masterlocks very easily. I can open most house deadbolt locks, but they might take me a few hours to figure out... Each lock is like a puzzle. The better you are, the easier you can figure out the puzzle.
It would be impractical to try to teach on a wide scale, and say "lockpicking is a fire/ems skill". You can learn to pop open padlocks pretty easily, but to actually become good enough to open "real" locks quickly (modern exterior home door locks) takes tons and tons of practice. And just forget about picking car doors. Very very difficult and easy to damage things - even professional locksmiths often won't do it except for fun as a challenge (there are better ways to get into a car).
Tons of practice to learn a skill that can be done faster by a snap gun most of the time. Picking a lock correctly should not damage it. Snap gun has higher chance of damage, but meh...
If it's legal for you to do in your state and your employer is cool with it, I could see it being a useful skill to have on rare occasion. I would be really worried about randomly getting sued, though, personally. It's outside our scope of practice, meh.
It's a fun hobby if you get into it, but I don't think it really has much of a place in EMS/fire due to 1) legal issues and 2) how difficult the skill is to learn compared to how useful it is (and you would need to be really good for it to be of much use in the field).