I'd like to add my "tuppence worth" to the post by DFC. Heading out over water, while it is a very tempting idea, would require the pilot to assess the risk associated with the existence of a super tanker, aircraft carrier, or any similarly tall vessel, crossing the extended centreline of the runway at the critical moment.
How high will the aircraft be at that point?
How tall is the ship?
Where, exactly, is the first point where the risk exists?
And then, of course, is there any possibility of the existence of an amphibious aircraft operation at the critical time?
Of course, as DFC suggests, even without such a problem, how high is the aircraft going to be in the first couple of miles? How much time will there be to go thru a ditching drill and get the pax ready for that?
These might be some of the reasons why an emergency procedure avoids going over water for anything but the shortest possible time.
As for the reference made by autoflight that "There are a lot of controllers, pilots and aviation authorities with their heads in the sand." I think it needs to be said that there is no clear way for ATC or regulators to predict the climb performance of any particular aeroplane in any given emergency situation. If pilots actually want these emergency procedures to be standardised, it will undoubtedly have to be taken up with ICAO (for Pans Ops) and the FAA (for TERPS).
And, even if you can get those two to actually agree on a standard forumula, it is likely to cater for the worst case scenario only. And that will undoubtedly result in a heavily reduced payload for most aircraft. This whole argument can go around and round and I can't say that I have any suggestions on ways to improve the situation - I'm sure that I'd be a millionaire if I could do that.