First of all, I would not argue for "Game of Thrones in space" because that wouldn't allow for 30 year old fans and their kids to enjoy it together, as you say. But, Star Trek has done little in the way of reaching that younger generation. As odd as it sounds, GoT and Walking Dead, for all their gore, are still able to garner younger attention, even if they are not watching it.
Why?
Walk in to Walgreens or K-Mart and head to the toy section. You won't find Star Trek there, but you will find GoT figurines, and Walking Dead dart guns. So, it doesn't have to be the TV show that garners that attention of the younger crowd.
Why is it a disadvantage of trying something different? I know that Star Trek has a certain flavor, and that attempting something new is considered problematic (see the "Not Star Trek"
@Balok's Decoy mentioned in response to me) but I still think that it needs to be attempted.
Look at Battlestar Galactica and its reboot. First of all, it was off-putting for me because I grew up with the original series and this was far darker, far more depressing and not the characters I knew. But, it garnered some attention among my friends and was successful for a couple of years. It drew in a newer crowd.
Now, to be clear, I am not advocating Star Trek as dark and gritty, or a new-BSG survival reboot. I am using it to illustrate a reboot that can be done. Star Trek could go through the reboot, a full one, without connection to prior materials, but still having the familiar look of the franchise (ship shape, uniform, terms, etc).
Even ST09 did not fully separate, and there is an argument to be made that a full reboot might have done even better.
Of course, as long as existing Trek fans keep having kids, there will always be an audience. I have long joked that TOS fans will end up as a future Catholic Church, and TNG fans will end up the Protestant wing.