I can think of several reasons that I wouldn't take one of the youngest members of my family to see the movie. The
PG-13 rating would've been the first reason.Along with:
1. The light and soundshow that was the destruction of the
Kelvin.
2.The death by sharp pikey thing impalement of Badass Capt. Robau.
3.The bloody barfight.
4. The multiple deaths on the drill platform of death: burning, impalement, and semi-defenestration.
5.Torture scene involving ugly bug shoved down Pike's throat.
6.More bloody fisticuffs with Kirk.
7.Too much loud noise and special effects.
8.Massive abuse of the laws of physics. (Okay, that one's a personal quirk

)
Implied sex scene with two consenting adults?
Brief depictions of attractive people in their undies? Compared to the violence and possibly scary scenes of the others, that wouldn't have even gotten my attention. But I imagine that whoever rates movies would include that with the others,(except #8) and therefore gave it a PG-13 rating.
Kirk just having sex? That's practically canon. Including implied sex with a pleasure slave, implied sex with a robot, and multiple times of no shirt, and ripped shirts, and torture- and that's just in TOS.
Trek without sex has never existed, although it's never been graphic. And even if that scene was excised by magic elves, I still wouldn't let the little kids see it. All of reasons 1-7. But if it had been a squeaky clean, G-rated unoffensive movie,
I would have only seen it once, not multiple times.
There are venues that have increased their profitability by becoming family-friendly, but I know of one event that shut down because of that. A PG-13 event that tried to appeal to everyone and failed miserably. Deservedly -they didn't know their audience. Trek is like that. It was never meant for kids, even if kids do like it. I'm not a child, and everything doesn't need to be made with them in mind. Clearly Trek was not meant for them.