Nope, I don't think it should be as important, at least in sports or maybe especially in sports! To use an analogy, would we watch over our son or daughter taking a test in school and "hang" on every answer? I think one point of the article is that far too many parents might answer that type of question "yes." Why? Because when their child is entering 5th-6th grade the parent is focused on HS and beyond. In our area, that includes goals for Stanford, Yale, Columbia, Harvard, Princeton and the like.
A baseball field is a very special place for our sons, in my perspective. None of them ever want to disappoint their parent. Too often they put plenty of pressure on themselves trying to please the parent. They want us to be proud of them, their performance, the hits, etc. I can already see this with our 2 year old grandson. His Dad is a college baseball coach. His Grandfather(me) is one who loves baseball. Last week he came for a visit, found the bat and ball and wanted me to soft toss so he could hit(left handed.) As we were "hitting," I talked about how his Dad was a really good player who loved baseball. From a 2 year old came the words "I love baseball too grandpa."
For a parent who hangs on every pitch/play, it is extremely challenging not to let the success or failure generate our reaction of approval or something different.
Just my opinion but we as parents are provided a special trust for our son's when it comes to sports and especially baseball. Baseball is a very cerebral game. It is also, at ages up to 15(ages 12-15 on the regulation diamond) a slow sport where "failures" are exposed for all to see, where the player lives with that failure until another chance to succeed might come his way. A parent "hanging" on every pitch/play can only enhance that high and especially the low, in my opinion. I know and did that with our son during his 12 year old All-Star tournament.
From that one play when our son was 12, I much better understood my role as his parent and his role as the player, athlete and competitor. From that point in coaching him and his senior league team through age 15, I was a much better coach and parent because I let them play, let them invest in the competition and the W's and L's. My role was not to hang on every pitch. As his/their coach, my role was to watch each pitch and "coach" the fundamentals no matter whether that pitch/AB was a success or failure. As his Father, my role was to make sure he was at every practice(early) and every game(early) and to support him in any extra ways he wanted and to provide input, when asked.
By age 15, he played the game at a level I never could. From that point forward, what he earned from baseball was based on his talent, effort, level of commitment and dedication. My role was to guide, when asked and certainly to guide or support if something went sideways.
These last few days with the HOF discussions are fun for me. One of our sons lowest and highest days in baseball occurred on the same day. Early one Spring Morning he called in the deep dumps after learning he would not get a full season assignment in Milb in his second season. He was devastated from a baseball perspective and it was tough to offer what would be "real" help. About 3 hours later he called as the AAA bus was arriving at Legends Field in Tampa. Turns out the AAA coaches put him on their roster for the day, he was starting at short and leading off, and the Yankee starting pitcher was going to be Randy Johnson tuning up in his final ST appearance. The excitement in his voice was screaming through the phone. He used 3 AB's off a guy who will be a HOF'er today to do what it turns out the AAA staff wanted to happen-get an assignment and roster spot when ST broke the following day. As he had done since that one game when he was 12, he worked his AB's against Johnson. There was nothing I could do for him when he stood in against Johnson, just as there was nothing I could do for him when he stood in that batter box against every pitcher from the time he was 13. What he did in each AB was "his" success or "his" failure and his opportunity to live and learn from it until the next AB.
Rather than "living" on every pitch, I truly learned to cherish the opportunity to watch him compete and watch him earn everything which happened for him in baseball.
Just my view, but there is a very big difference between my role as his parent and his role as the athlete/competitor.