A player can only be attacked when she is offline. Hardcore trophy hunters are online most of the time, because trophies are mostly gained in offense, not in defense (some gemmers even ignore upgrading their buildings). Thus it can take a while for high trophy players to be given a match when they are attacking. Players complained about the player base being too small to support trophy hunters, when the game came out in August 2012. Trophy hunters kept complaining, and the most SC did was force players to logout at least every 8 hours.
The fact that players can only be attacked when offline has another consequence. When a player logs in while under attack, she does not see what is going on. Instead, she is given a loading screen for up to three minutes. This is inelegant, and it could be improved.
As others have noted, in Clash of Clans, the clans don't really clash. Players of the same clan can not gang up against a rival clan. The only thing they can do is chat together and donate troops to each other. Some even say that the game only provides the illusion of a multiplayer game. Players can not even choose who they will attack. The system gives them villages from other players one at a time, and the player has to next sometimes for 10 minutes to find an appropriate target.
Match-making is also SC's way to remove churners from the game. Churners are called
inactives in the community. Inactive bases have full mines, so they provide a lot of loot for little effort. To keep the loot in check, SC removes inactives from the match-making queue every few weeks. Players notice it very quickly: one day, they loot 300k gold per raid on average after 30 seconds of nexting. The next day, it takes 10 minutes of nexting for a 150k-gold raid. I think a lot of players stop playing when they suddenly can't find loot.
Retention and monetization
Achievements such as unlocking the Dragon, reaching a certain amount of trophies, or looting 100M gold, all reward the player with gems. These gems are the only way to acquire builders to speed up the upgrading of buildings. Thus for players who do not spend real money to buy their builders, these achievements are long-term goals. For many players, the game is about the journey, not the end. Achievements also work in the beginning as quests guiding the player through the basic game mechanics.