My experience as a player in a few maritime adventures is that they tend to take away player agency. The captain makes you tend to mundane tasks, you get blown far off course and stranded, you watch fellow party members get keel hauled, you get trapped in tight quarters combats by raiding parties and can't escape short of diving into shark infested waters, you leave behind all the contacts you had on the mainland and connection to that campaign world, you're basically trapped in a floating hamlet where everyone knows you (bad for rogues), you're usually at sea for months with little happening, it typically involves several boring sessions of preparation just to launch the expedition, there aren't good rules for it in the core books (and thus it's out of the scope the core game can handle), heavily armored characters sink and drown easily. I could go on.
You're right about heavy armour - it doesn't work well at sea and should likely thus be eschewed by PCs.
Other than that, however, I could work around most of your points with relative ease. First, if the PCs own the ship and either crew it themselves or hire the captain and crew it's less likely they'll be swabbing decks all that often and almost certain they won't get keelhauled. The lack of good rules means I just have to make up my own; not like I haven't already done that for almost every other aspect of the game, so no big deal. If it's a maritime campaign from the start or close the PCs aren't likely to have many mainliand contacts of importance to lose; or they instead have contacts in multiple ports rather than all in one place (and their connection to the campaign world is the sea). The rogue's going to have to do her thieving in port rather than on board, but that's no different than doing her thieving in cities rather than while travelling overland with the party.
As for being trapped in tight quarters and-or having to dive into shark-infested waters, those are just acceptable risks. And keep in mind when you attack another ship you're inflicting those same risks onto your foes - it goes both ways.
Being at sea for months with little happening isn't a problem provided those months go by fairly quickly at the table. Could be as simple as "Players: We're fully geared up and ready to sail. We'll go west unless something catches our attention otherwise, and if we make it to the land of Injuli we'll decide from there what comes next." DM: OK. You leave port on April 6 under fair skies and steady winds. <
rolls some dice> On April 12 the weather turns foul, with a storm coming from the north. What do you do?" {{{
role-play through dealing with storm}}} DM: "Carrying on, on April 24 you see land to the southwest, probably an island. What do you do?" {{{
players decide what to do, maybe the island gets explored}}} DM: "Your voyage continues. On April 28 at daybreak you see the sails of two ships to the northeast. It soon becomes clear they are faster than you, and they've altered course toward you and are approaching fast - as things stand they'll catch you within the hour." {{{
party have to fend off some pirates}}} Etc., with time allowed all along for inter-character discussions and RP as and when desired.
And that could all be just one session, or more if the island exploration led to anything involved; and you've been at sea three weeks already.
