Clash-of-clans – Clash of clans production rate

Besides the rewards you already mentioned, there is a bonus for every raid you win that is based on what league you're in. It's usually small, but it can make a difference.

There's also the same reason there are leaderboards in any game - to see how you stack up against other players!

There is a downside to having many trophies, and that's that trophy count is an important factor in matchmaking. Thus, if you have many trophies you're going to get raided often by high level players, and you're likely to get matched up against hard opponents.

Many players that I've seen will try to maintain or lower their trophy count in order to find easier players to raid. You've probably seen players dropping trophies in this manner - usually, they will deploy a single troop against you, or they'll put out and immediate recall their hero units.

The Clash of Clans Wikia has a breakdown of all defenses and their damage rate per shot, including the splash radius where applicable. For instance, see this page for the Mortar.

At level 1, the Mortar does 20 damage per shot (= 4 damage/sec) with a 1.5 tile splash radius.

I don't want to completely reproduce their tables, but you can get an index of all the defensive buildings on this page.