I think you slightly underestimate how much work and expertise it is to build ships that can transport an army over a long distance on sea.
This isn’t what the Sea Peoples built. It isn’t even what the Romans built. Most Mediterranean cultures lacked the navigational and ship-building expertise to let the shore out of sight. That doesn’t mean they didn’t need skill. But it was less skill than needed for metallurgy, in part because the latter’s inputs are dearer.
Making a boat that can carry multiple people on sea without sinking when the weather goes a little sour (which can happen in less than an hour in the Mediterranean) is a very hard thing to do. And if you know how to do that you'll never have any shortage of metal or other goods in the first place because you end up being the one who trade them for profit.