No, that was not the reason. CBS and Paramount were split at the time, and CBS did not want their TV viewing audience to think that their new show had anything to do with the KT because that was Paramount's sandbox to play in.
Now with that said, DSC's visual style sure did look a lot like the KT, despite CBS's want to keep them separate. And what DSC absolutely did not look like was a prequel set ten years before TOS, which further added to the confusion that CBS was trying to avoid.
