Why should I use a bound sword?

There are a few reasons why you would want to use one:

1. It saves you weight from not having to carry one around.
2. Like you pointed out, with perks, it can automatically soul trap an enemy, so you can use a better weapon unless you need soul trapping.
3. With even more perks, you can banish summoned enemies. Note both of these can be reproduced via enchantments, but this way you don't have to recharge your weapon.

The drawbacks:

1. Yes the base damage is high, but you cannot improve a bound sword via smithing, so the damage is really quite low during the end game.
2. It lasts only so long, then you'll have to recast.

All in all, like you said, the lack of damage does become a big issue once you start investing into smithing.

The 14 is base dmg which means that it changes as you level up one handed! It has 14 dmg if you are lvl one in one-handed.
14 is A LOT of base dmg; in fact, it's the second best sword in the game as a daedric sword has 15 base dmg. So basically it's a good sword but at higher levels you may want to start using weapons and magic like a battlemage. Please remember bound weapons do Less damage to dragons because dragons have magic resistance.

For mages, there really isn't a point except to farm souls for soulstones. As a mage you want to keep your distance from your enemies. Plus, as a mage, your skill in one-handed weapons won't get as high to take advantage of the the skill bonuses. If you have a big ugly in your face, I think you're best off with some sort of enchanted weapon instead.