As far as I know the only actual benefits from trophies are:

* The top 3 clans top 10 players receive some gem bonuses when ever a season completes
* There is the "Sweet Victory!" achievement which you can complete by obtaining 75/750/1250 trophies.
* And then there is the League All-Star achievement that gives you some gems as you reach those higher level leagues (250 for Chrystal, 1000 for Master and 2000 for Champion)

So, unless your clan can seriously compete of a position amongst the top 3 clans, then you have no incentive to maintain a high trophy count. You may want to temporarily rise it to get some gems from an achievement, but only temporarily.

So am I missing something or what's the point?