As the Wikipedia article on Sea Launch says, there are some major advantages to launching directly on the equator (maximum performance to geostationary orbit) and some secondary advantages to launching in the middle of the ocean (mainly improved range safety).
But launching directly on the equator doesn't require launching from the ocean, and you can also avoid most range safety problems with a careful selection of your equatorial land site. ESA's Kourou site already does quite well on both counts, and it's hard to see how any additional gains are really worth the logistical hassles of launching from floating platforms far from any land and fixed infrastructure (communications, tracking stations, air strips, fuel depots, etc). Aside from getting all that hardware and propellant from port (Long Beach, I think) to the launch site, your launch crews are bottled up on ship for weeks at a time. Even in Kourou you can go to the beach or sightsee (e.g., to Devil's Island) on your days off. Although I've never been there myself, my friends who've been on launch campaigns seem to make a big deal out of them, and I think it definitely helped them stay sharp back on the job.