The game is fun for the first day. Then you're sat around waiting for the chests to unlock. It's like the developers don't actually want you to play the game. I think more people would buy gems if the unlocks were about 25% less time.
It's a common complaint and it used to be worse! In beta there was a gold cost equivalent to arena level (i.e. 1g at arena 1, 2g at arena 2 etc.) for EVERY battle. As gold is so hard to come by at the beginning, it made saving up very hard and therefore the incentive to do battle when all chest slots were full was even lower. There was even a cost of 5g for friendly battles. Fortunately they removed that and for me that was the only limiting factor.
The incentive is trophies, the more you get, the higher the arena you will be in. Higher arenas give you bigger chests, with more cards and money, as well as the possibility of unlocking new cards that are only available in that arena. There really isn't a reason not to push on.
As you progress, it will bother you less. The timers annoy everyone at the beginning as progress feels slow, but that tends to ware off... honestly it does!
Grinch