Your highest-level class can pick up EXP from the story, which doesn't get doubled for lower classes so you're not missing out on anything by doing that.

I feel like the game has a good pace of quest EXP. You can level one class almost entirely from running MSQ and sidequests, while using a second class for your daily roulettes, and keep pace with the story quite nicely at that rate. (I'd suggest keeping your highest class two levels above the current story quest level, so you don't get caught out and unable to accept the next quest.)

There's not a lot of use to getting a character quickly to Lv60, because there's not much you can do with it! High-level content is all locked behind story progress so the only thing it would get you for now is instant access to the red mage and samurai jobs. (Definitely don't buy level boosts for those. They start at Lv50.)

The other not-entirely-an-advantage of buying a job boost is if you particularly wanted to play one of the jobs locked behind the Heavensward expansion: astrologian, machinist and dark knight. But as you say, it means you'll miss out on the story attached to those job quests, and I enjoyed those particular ones - astrologian and machinist anyway. I haven't played dark knight but a lot of people say it's their favourite. It gives a darker slant to your characterisation though, and I didn't like the sound of it for (my idea of) my character's personality.

But still, it does take a long time to level up everything. I've been playing for a bit over a year and have just about finally gotten all my battle classes to Lv70 - though I've also got a couple of alt characters that I've been spending time on as well.