Louise is the first of the humans to begin to experience time as the heptapods do because she's the first to truly begin to understand their language. We clearly see she goes on to teach it to others, but Ian probably just didn't ever learn it.
Someone in a Tree, for more clarity, we hear Louise talk about the Sapir-Whorf hypothesis, which is the idea that the language someone speaks actually changes the way their mind works. The heptapod's language is nonlinear, and they experience the world in a nonlinear fashion that is entirely different from how humans experience it.
It's certainly a double-edged sword of a gift. Louise clearly felt the experience of loving her daughter so deeply that she chose not to alter her path. When she asks Ian if he would change his future if he knew it all, he said that he wouldn't, and that he would instead know to savor the best moments of his life. I think this is probably how Louise came to appreciate the gift: she was able to use it to savor her life rather than fear the future in some way. (I think that's probably also why she eventually told Ian: he said he'd savor it, too!!)
The really interesting thing (for me) to think about is how the heptapods have never known anything differently. It's how their language developed, and they've likely been experiencing time this way for millennia as a race. They probably have just as much trouble thinking of how not to experience time this way.
I don't think that I would want it for myself -- the worst part would be seeing a future I couldn't change. But I can see how Louise found some value in it. I think it's especially important to consider what we see of her at the beginning of the movie: she seems to have little meaning in her life. We think it's from the loss of her child, but this was her life before her experience. She shows up at work even when there are aliens outside. She tells her mom "Oh, you know me, I'm always fine" when her mom calls in a panic about it. There's a darkness and gloom over her life. I'm not saying she was cured by loving her daughter, but I do think that perhaps something fundamentally changed in how she looked at her life.
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