If you cannot understand why a character couldn't just luck into open a lock, you should apply the same forethought into understanding a trained thespian cannot simply pick up an instrument and play it.
Going on from those 2 points - the first is are you suggesting modern locks have not progressed in the past 1000 years to the point an untrained person who would've lived in an era when picking locks was probably far more likely, since security codes and passwords were not around? You have to remember things would've been far different, and while an adventurer was "untrained" in picking locks, it would be assumed they could have some experience in dealing with it from time to time, maybe their key broke at home to a chest and they couldn't afford a replacement. So when it comes to certain untrained skills it's not like some kid who goes to school and then plays video games is trying, it's about adapting the situation to a period wherein a lock was technologically advanced (I guess consider it on par with someone untrained learning to code themselves).
Going on to Perform, performance (as you said) is a natural talent for coping with crowds, it's about delivering the scene in an entertaining and dramatic manner. Musical Instruments can be used as part of a performance, but this is where a DM could decide if you're not "performing" but merely putting on a performance, you might use (dexterity) musical instrument as you're attempting to play a very manually dextrous piece on your violin.
Ultimately it is up to the DM how they allow players untrained in a skill or tool to act - sometimes denying them a roll while other times they might just have a basic chance of something happening. I would expect many DMs not to let an untrained person attempt to use a tool, such as thieves' tools, because a player is unlikely to know what to do with them, but may allow them a straight dex check to open a lock somehow (and simply alter the DC). One thing I do think is a lot of the time people use "Disadvantage" to mean "The DM isn't sure how to alter the DC of the check properly" as Disadvantage is more you have a temporary impairment, not a permanently crappy chance. Disadvantage is best used when you are intoxicated and trying to lie, or attempting to pick a lock with 1 broken hand, as opposed to using it when you don't have the appropriate tools (which, in essence, is not temporary it's a permanent lack of the correct tool haha)
As for Deception and Performance, consider the TV show Leverage and Gina Bellman's character - a terrible performer on stage, but an amazing grifter (liar) off it. If you wish to use a performance to deceive, it's no longer a performance and simply becomes a deception check, it may involve flailing of the arms and a bit of acting, but acting is a division of performance that can also be used during deception as well.
Thieves' Tools probably seems more strange because you picture the modern day set and assume back then was similar. Technology, all technology, changes over time and picking a lock back then is not the same as doing it today - even if based on similar principles.
Going on from those 2 points - the first is are you suggesting modern locks have not progressed in the past 1000 years to the point an untrained person who would've lived in an era when picking locks was probably far more likely, since security codes and passwords were not around? You have to remember things would've been far different, and while an adventurer was "untrained" in picking locks, it would be assumed they could have some experience in dealing with it from time to time, maybe their key broke at home to a chest and they couldn't afford a replacement. So when it comes to certain untrained skills it's not like some kid who goes to school and then plays video games is trying, it's about adapting the situation to a period wherein a lock was technologically advanced (I guess consider it on par with someone untrained learning to code themselves).
Going on to Perform, performance (as you said) is a natural talent for coping with crowds, it's about delivering the scene in an entertaining and dramatic manner. Musical Instruments can be used as part of a performance, but this is where a DM could decide if you're not "performing" but merely putting on a performance, you might use (dexterity) musical instrument as you're attempting to play a very manually dextrous piece on your violin.
Ultimately it is up to the DM how they allow players untrained in a skill or tool to act - sometimes denying them a roll while other times they might just have a basic chance of something happening. I would expect many DMs not to let an untrained person attempt to use a tool, such as thieves' tools, because a player is unlikely to know what to do with them, but may allow them a straight dex check to open a lock somehow (and simply alter the DC). One thing I do think is a lot of the time people use "Disadvantage" to mean "The DM isn't sure how to alter the DC of the check properly" as Disadvantage is more you have a temporary impairment, not a permanently crappy chance. Disadvantage is best used when you are intoxicated and trying to lie, or attempting to pick a lock with 1 broken hand, as opposed to using it when you don't have the appropriate tools (which, in essence, is not temporary it's a permanent lack of the correct tool haha)
As for Deception and Performance, consider the TV show Leverage and Gina Bellman's character - a terrible performer on stage, but an amazing grifter (liar) off it. If you wish to use a performance to deceive, it's no longer a performance and simply becomes a deception check, it may involve flailing of the arms and a bit of acting, but acting is a division of performance that can also be used during deception as well.
Thieves' Tools probably seems more strange because you picture the modern day set and assume back then was similar. Technology, all technology, changes over time and picking a lock back then is not the same as doing it today - even if based on similar principles.