Well, I do the same thing as giulio, its hard to spot incomming fleets anyways unless you have a enormous fleet or the will to keep using recon with airships or something similar. When you see a enemy fleet near your cultural borders its very easy to quickly move some troops around and maybe draft/whip/buy yourself some more defenders. Unless your really far behind on techs your defenders should easily be able to kill a dozen of troops who are suffering from the amphibious attack modifier (unless they land first, but then you have more time to get a defensive army).
It could also be much easier to destroy those invasion armys if your playing on normal (like i am) instead of marathon, its pretty easy to get 5-6 rifleman trained
in 2 turns without drafting (the time you usually have after spotting the enemy). And well you should have had some defenders before they came anyways.
1. Escorting troops to that other continent after the initial landing/amphibious attack. Typically, my marines keep plundering the enemy coast even after the armor is pushing inland, and both columns will get reinforced until the war is in its winding down stage.
2. Heading off enemy amphibious invasions. The AI will not send unescorted transports at you. If I'm at war with an AI on another continent, I can wage that war very cheaply by just sending over a few attack subs and picking off his escorts as soon as they leave a port. I'll catch several of them alone on their way to the invasion launching point, and if they ever do get a stack together and out of the port, I can worry it to death with the subs over 2-3 turns, until it's no longer any threat.
3. Allowing myself to keep working sea tiles, taking advantage of seafood and garnering intercontinental trade routes, while depriving my enemy the same. This one's self-explanatory. Control the sea, and you can exploit the sea. Allow the enemy that control and you're at his mercy in that respect. The importance of this depends on how heavily you rely on sea tiles, obviously.
4. Hammer advantage. The AI wants to control the sea or break your control of it. The AI will, therefore, spend hammers toward that end. With a little forethought, you can spend fewer hammers in order to make sure he keeps spending hammers on a navy, and make sure that said navy never achieves that goal. This either increases your production advantage or decreases the AI's, depending on the situation. Either way, the end result is that you have relatively more hammers compared to the AI than if you had not exerted control over the sea.
Hmm you have some good points there but im not convinced yet, I dont use 1 since ill be attacking with 2 stacks and the enemy will be conquered before my fleets have the ability to sail back and forth (with a reasonable distance ofcourse). I explained 2 before in this post.
3. : Wars are usually blitz wars in civ (well they are for me) and destroying work boats during wartime will give you only a very minimal bonus during wartime (their citys will grow less or they switch tiles and lose a few hammers to maintain the same growth).
Youll have to rebuild those workboats once the land is conquered though, so destroying boats will cost you hammers in three ways, once for the boats youve sacrificed to gain control, once for boats you have to remain control and to actually destroy the workboats and once for rebuilding the boats. Its simply not worth it for me.
Having control does make sure your own workboats are secure, but at what cost? You spend hammers to get and remain control while youll only have to rebuild 3-10 workboats which doesnt cost that much compared to those boats.
4.: When not at wartime you cant gain control over the seas unless you spam privateers (which is bad since they cost too much and die too easily for that). So youll have to destroy the enemys fleet when the war starts. Lets assume you succeed in that. The enemy civ will now build some ships in his coastal cities, not all of them since hes under attack at land aswell and he has most likely lost a good amount of defenders. So lets say he builds 5 ships which could have been rifleman. The only difference you really made during wartime is that you have to face 5 rifleman less, although thats usefull I think you could have spend the hammers for your ships in a better way, by building a few extra cannons for example.
If you completely ignore his fleets youll have a hammer advantage above the enemy aswell since he spent tons of hammers o getting a betetr fleet then you while you spend it on more usefull things, like a few new shiny cannons.
But maybe your fighting more longterm wars? In that case naval becomes a whole lot more attractive, point 4 starts to shine since your not talking about 4-5 boats he rebuild but over complete fleets of them. And destroying workboats is obviously more usefull during longterm wars.