The relationship between gymnast and coach is tricky - Of course, these kids bond closely with their coaches - especially when the relationship lasts years. Often the coaches are only 10 or so years older than the child, and can see themselves in the kids. We parents also spend so much time with this sport it does feel like we are all connected beyond the gym, and of course we often have lots in common.
As a pediatrician, I often have to decide where the boundaries are with patients and families. I do not friend patients (teens), even if they are kids I've mentored in the clinic, etc. I'm careful which parents I friend also - making sure they are people I have a natural bond to other then my job (our town is relatively small and I've worked here 13 years). It's just a matter of being able to do my job well with the appropriate boundaries.
Many coaches are excellent at walking that boundary well. DD and older DS have their coaches numbers to text if they'll miss practices, have questions, etc. Also , DD has emailed her coach specific questions at times. She also has contacts with a couple of past coaches when they come to town (as in she and friends WITH THE PARENTS PRESENT have gone sledding, etc with old coaches). I still read all her texts, and she isn't 13 so no social media yet....
In the past 2 years our community has had a trusted gym coach jailed for sexual abuse and drug use, and one who had very few boundaries with athletes suddenly leave town after lying to the kids for a years - to the point of telling them their parents were the ones lying, drinking to excess when traveling as supervisor to teens/tweens and leaving them alone with an opposite sex coach all night, etc. Told DD she was her "second mom" for years - and same with many other kids. I realize these are the actions of individuals - both of whom clearly were troubled beyond the average gym coach - but had clear boundaries been established by the gym organization as a whole and individual parents as well, many fewer kids would have been hurt.
Parents were easily swept away over the years into trusting these people unquestionningly - my DD was never alone with her coach other than private lessons (usually but not always with another adult in the gym), but many kids traveled with her, and she actually lived with several families over the years. Now, there is great good in most people along with the bad - but in the end we parents need to protect our children, and our children (and yes, teens are still children) will usually only see the good....I want my kids to love and trust their teachers/coaches and feel safe with them - but I want them to be able to separate themselves from them, realize that they are not FRIENDS or FAMILY....they are teachers/coaches. They may love the athletes and the athletes love them - but only in so far as that relationship goes. Its quite simple to have a team facebook page (or instagram feed, etc) with coaches, older athletes and parents where info can be shared appropriately. Responsible coaches will allow appropriate access while limiting it.
I have no issue with kids and families stepping over those boundaries once the coaching relationship is over - but remember these are KIDS - My DD (12) recently had a young male coach in his 20s move on (as had always been planned). He was a very effective coach for her - she has all brothers and uncles, and her dad is not in the picture much at all - his easy going faith in her and ways of getting her to go for things "vault is like riding a bull - scary as can be for 8 seconds than its over"...really worked well for her. She misses him like any tween girl would - and has exchanged 3 texts with him - about his trip, her bars and "good luck" - all of which I've read, and all of which were AFTER he left (same with all the other girls at the gym - actually - he was well loved and wise - made a point of planning ahead with parents and head coach of how to negotiate all the tween/teen girls who wanted to stay in touch). I know as her mom its a normal preteen crushish thing as well as a good coaching relationship - and so does HE...but it was also a very healthy teacher/coach relationship for her and the boundaries are very clear. However, had he not left and she wished to text him about non-gym things, or friend him (if she had social media), or didn't have me reading her texts/discussing with her boundaries, etc, it would not be healthy. In a few years I won't read all her texts/posts - and she won't want me to help her figure out if its ok to send one or not. I did not recognize how powerful her relationship was with her past coach until the trust was broken and opened up so much for her that she's still only 9 months later beginning to trust her new Head Coach and getting back to learning new gymnastics (which I see as a sign of moving on in life - its more than gym they learn from the coaches!). When she was 9 and seemed to have a close relationship with her coaches I thought it was great - she is a special girl (to me) and when they led me to feel that she was a special gymnast of course I was flattered....more red flags would fly now.
All this is to say that NO, I don't think its harmless in any way to blur the boundaries between coaches and families/athletes. Yes, I do understand that friendships are made and that after one relationship is over the other can flourish in a healthy way. And yes, I feel "friendly" with my kids long term coaches, know their kids outside of gym, etc....but a healthy community (gym or otherwise) requires boundaries - and the parents and coaches need to be teaching the kids how to establish those!