A level 5 rogue will quite probably have a thievery dc of 13, if they invest in it and max dex. The average lock has a dc of 25 and requires 4 successes. It takes a roll of 12 or better to have a single success, and will average about 9 rolls to rack up those 4 successes. With 9 rolls wherein you crit fail on a 2 or lower, the likelihood of breaking a pick is ~61%.

Should a level 5 rogue take a minute to open the average lock, and more likely than not break a pick in the process?

And let's look at a good Lock: DC 30, requiring 5 successes. The level 5 rogue will only succeed on a 17, meaning it will take on average 20 attempts to get those 5 successes. On one attempt in a thousand our Lvl 5 rogue will open this lock before breaking a pick, and will typically break 3 in the process.

Am I missing something?

Warlock wielding shadow blade. Obviously there are stronger things to concentrate on, but do your worst within parameters.

Minor illusion:

You create a sound or an image of an object within range that lasts for the duration. The illusion also ends if you dismiss it as an action or cast this spell again.

If you create a sound, its volume can range from a whisper to a scream. It can be your voice, someone else's voice, a lion's roar, a beating of drums, or any other sound you choose. The sound continues unabated throughout the duration, or you can make discrete sounds at different times before the spell ends.

If you create an image of an object--such as a chair, muddy footprints, or a small chest--it must be no larger than a 5-foot cube. The image can't create sound, light, smell, or any other sensory effect. Physical interaction with the image reveals it to be an illusion, because things can pass through it.

If a creature uses its action to examine the sound or image, the creature can determine that it is an illusion with a successful Intelligence (Investigation) check against your spell save DC. If a creature discerns the illusion for what it is, the illusion becomes faint to the creature.

-Physical interaction with the image reveals it to be an illusion.

Not an action spent physically interacting, but physical interaction. An arrow strikes the image? Revealed to observers. You use an object interaction to touch the illusion? Revealed to observers.

-If a creature uses its action to examine the sound or image, the creature can determine that it is an illusion with a successful Intelligence (Investigation) check against your spell save DC.

If, not only if. This could reveal the illusion without physical interaction, and is particularly useful if the illusion was behind a window of out of range.