There is certainly no wrong or right way to play. But my take is that by giving them X uses of their background per session, or per day, or whatever, you're essentially turning the use of Backgrounds back into a resource to be strategically managed. You're telling the player they get an X% worth of bonus percentage points towards your successes today, better use them judiciously. So, I can see why from your perspective you might consider it a rules abuse if the player gets what you feel is a free unlimited use of their background.
Nothing wrong if thats the way you like to play. But that's not how I perceive the game was intended to work. Which is not about backgrounds being a game resource to be managed, but more about an enabler of fiction. I've posted this before, but the players getting their bonus every time isn't the problem, its them getting the bonus every time but making it routine and boring.
If the players get the bonus every time, but the game is interesting and fresh, then who cares? That's really the point of the game. Also, mechanically, even getting the full +5 bonus just drops the difficulty by one degree. There is still a chance of failure. But again, with Fail Forward, the emphasis of the game is on making things interesting, not on beating the resource management mini-game by hoarding your daily allotment of background usages for when you need them.
Now if you like the resource management aspect of it, and you derive enjoyment from pulling out that bonus you had in your back pocket for when you need it, then more power to you. The cool thing about 13th Age is its really easy to house rule things to suit your tastes.