My experience at other boards with fleeting echoes what a lot of other people have already said. But typically, the main problems that I've seen at the past is people being ultra-competitive to the point of godmodding, or one small naval action draws a disproportionate response from another faction, which then stops the weaker faction from fleeting at all.
But there are ways around these problems.
The very first is to simply have an agreed upon outcome to better focus on the writing.
The second that I've used in the past where a competitor and I wanted to have a competitive game is to play the battle by mechanical means (typically by using Full Thrust rules, and then playing it out via dice) or back in the day, using Star Wars Rebellion's fleet mode via dial-up connection (but that only limits the battles to certain canon ships). Full Thrust rules and ship designer programs for it are available free on the net, and while it is some work, the mechanics are basic enough that people generally can figure out the basics of how to play in less than 15 minutes. If anyone is interested in trying it out with me, or has questions as to how it works, feel free to ask me.
Once the other player and i figured it out how the battle unfolded by that simulation, we'd simply write it out, allowing us to focus more on the actions and story of the battle rather than being Uber-god players bent on beating out the other person.
Fleet sizes or 'How to stop Apprentice Bob showing up with 5 command ships'.
This could be done with a meterage cap. For example, set that you can only have up to ~1600 meters of capital ships present at a battle. That means that Apprentice Bob might arrive with one ISD (1600 meters in length), while his opponent shows up with five Nebulon-B frigates (300 meters in length for each of them, for 1500 meters total). This has the side effect of also keeping fleet sizes down to things that can be easily matched.
The downside of this system is that it doesn't really account for strategic positioning, but for fun scraps or simpliticity's sake, it's the easy way.
How to actually do it or 'Do I really need 3 Excel sheets open for one post?!'
Limiting fleet size helps with this, but it's unavoidable to some extent. But if you do the battle mechanics all at once, it's not that bad, because you can do the battle in one sitting (if your opponent is online and talking with you as the battle progresses).
Ease of posting or 'Where am I on this 3D map again?'
While space combat is realistically a 3D battlespace, most battles that we see in the movies tend to be working 2D with a very limited amount of depth. That same holds true for most fleeting that I've seen, if nothing than for simplicity's sake. Full Thrust uses a hex map, and that's typically what I use for tracking my battles because it also helps with figuring out how maneuvers and speed also play into the battle. But again, you'll probably have to share the map along with your updated movements with your opponent if you want clean-cut play without any ambiguity.