What is the purpose of a deeply cut stud in interior walls?
It’s an old “sheetrockers” trick. When an interior non-load bearing wall stud is warped, it can be brought “back in line” by cutting it and relieving the stress.  

I’ve only seen this done on interior non-load bearing walls AND when there’s just one or two in any one wall. If you have several in a row or they’re in a bearing wall, you should consider reinforcing a few studs. 

If it hasn’t been a problem, I’d be cautious about fixing something that’s not broken. Banging the studs with a hammer could cause other problems.