The way it’s set up, they only last half an hour, and that timer counts even when you’re not in a match. That is a very small window of time. Only 2 and a half matches worth.
Considering XP is almost entirely tied to your challenges, you’re really unlikely to get a lot out of them. So many challenges require specific weapons or game modes that may not even show up in your matches during that brief half hour.
They should last much longer. At least 2 hours at a minumum, but I’d even push for 4 or more.
They should honestly just be per game. There’s no reason it should be timed at all.
The fact it’s timed means you’re getting less out of your purchase by playing longer games.
With the obvious response being that it is the way it is because of monetization, I doubt they will increase it to several hours.
That being said, a temporary fix (and one that would allow you to more adequately plan when to use one) would be to have an XP boost last for X number of matches. I would put it around 4 matches, which I think is a totally fair number, and, well timed with your weekly challenges at the start, should allow you to complete several and see a sizeable bump in EXP.
Here’s my opinion, I participated in the Rockstar promo so I have almost 40 double XP boosts. I think it would be a little unreasonable to be able to have 2XP for 160 hours (40 2XP times 4 hours each) I do definitely agree with you that its not good that they run even when you are out of a match. I think 45 minutes of in game time is a balanced solution 
XP boosters without match xp were dumb to begin with.
I mean, you’re not wrong.