I think the most important aim of balancing should be to try our best to ensure an increased number of competitive civs in this game (the highest number possible). In other words, most maps allow only around 3 civs at max to have a chance in a free pick game. If some changes can be done to push this number up to the highest possible, it would be great. Arabia is the easiest setting to balance IMO, and considering that this is the single most popular setting it is a good way to begin by trying to perfect arabia balance.Every unit currently has their place in this game, there is no unit except the Turtle Ship that is completely useless.
I don't believe in the add 5 hp to this, or 1+ attack to that unit changes. The best changes made are small adjustments of bonuses that are clearly OP, such as spanish trade bonus, vikings water, huns CA, maya economy, and the other things like stone walls that are way too strong for feudal age.
I dont believe there is any harm in trying to equate the overall power of civs (as vague as it may sound) as well as possible.
While as you said, every unit has a place in the game, many clearly have more of a place than others. Things like +5 HP, an increase in speed etc for longswords can simply improve their scope by whatever is realistically possible. There is also a reason why drush, palisades followed by early xbows is so common in the game. Something can definitely be done to prevent the strategic aspect of the game from being so stale. After all, the more the variety, the more the strategy options, the better is AOC.