When I first moved back home from college, I was looking for a place to continue training and found a Tang Soo Do school that also practiced grappling. I was a 1st Dan in Tae Kwon Do at the time. They figured that I would have good kicks, but once it came time to grapple, they would own me. The first time one of them caught and held onto one of my kicks, I was surprised because I thought they were doing tournament rules, not mixed rules. I quickly regained composure and clinched in, going for a neck tie up while stomping down with the leg that hand been grabbed. I then pushed the guy's right arm up and ducked under it, wrapping my right leg around his right leg, leaned over and grabbed his other with both hands. I rolled a little backwards and then spread his legs as far apart as they could go. At this point in time, he was completely surprised and had no clue what had just happened, only that his legs were being used as my Thanksgiving Day wishbone. After he tapped out and I let him up, he asked what I had done. I replied, "That was a banana split. I wrestled for twelve years before taking up Tae Kwon Do." From that point on, they knew that this was one Tae Kwon Do Black Belt that they could not just throw to the ground and watch squirm like a wet noodle.
I too think that Tae Kwon Do students should learn at least a little bit of grappling so they know what to do if they are ever caught off or knocked off their feet. They do not need to be champion grapplers, only know what they will face and how to get back up to their feet initially. If they want to learn more later, great. If not, at least they know what to look out for.