@1208Wither welcome to the forums! Glad you've joined us.
Here's the thing: Between the rewards for ranking up, league change rewards, daily challenges and ads, you can get quite a few gems per week if you're diligent. With the end of season rewards, you can end up with quite a few packs. EA has to walk a fine line. They have to give you a fun and rewarding game, but since it's free to play as much as you like, they also have to make those rewards trickle in at such a rate that you're at least tempted to spend money. If they did your suggestion, there would almost be no reason to pay.
Now I would like to see them so something along the lines of arena in hearthstone where you can pay an entry fee with the gems you have and play for increasing rewards depending on how far you make it. These rewards being gems, packs, legendary cards, and Sparks. This would allow people a way to get more of each if they're clever/lucky enough players; while also giving players another reason to buy occasional gem packs.