While it is true that healing magic doesn't heal a huge amount of damage you also have to remember that for the most part players also have surprisingly few hit points. 3-10 may not seem huge but considering the most hit points a character can have at 1st-level (barring feats) is 16 (Barbarian with 18 Con) it is more than sufficient.
At 1st level, yes. After that certainly no. A cleric has only access to other healing magic at 6th level until this point that can do the same.
As for having better things to do during a fight then heal - you've pretty much hit the nail on the head there. You really shouldn't be healing in battle - short of something unlucky coming up (such as a critical hit) you should focus on winning and patching you team up after the fact.
I agree, normally there are better things to do. It is always better to kill the enemy or protect against damage than heal damage. But that option was taken away, that is the problem.
I will admit that Second Wind is exceptionally strong for a first level ability though it really doesn't scale all that well unless your fighter is consistently rolling really poorly for his hit points.
You are 100% right. It can recover 100% at 1st level. At 20th, it can recover 15%, but you have 3 of those. It means a fighter can return almost guaranteed to 100% life from almost 0, when combined with recovery dices at least once per short rest and with luck or feats more. But it at least escalates, but healing magic do not.