Instead of just speculating, the NHTSA did an actual study on this, and they reached the opposite conclusion. They investigated crash rates in Tesla vehicles that had the original autopilot hardware installed, both before and after autosteer was enabled via a software update, and found that autosteer reduced accident rates by 40%.
When Tesla talks about how much lower their accident rate per mile is compared to other cars, that's kind of statistical bullshit, since there are plenty of other uncontrolled variables that are in play that could affect this besides the cars themselves. But in the case of the NHTSA study, they were looking at the same drivers in the same cars, and the only difference was that one day a software update came out and enabled autosteer, and suddenly accident rates went way down. That's pretty damn convincing if you ask me.
https://static.nhtsa.gov/odi/inv/2016/INCLA-PE16007-7876.pdf