Many year ago I used to sail with my Dad on the Solent. Going back far enough, the light ship used to be manned. All the boats going passed used to wave and usually get a wave back. Later on when the Solent became really busy with yachts I bet the lightship keepers asked to be taken ashore from being fed up with waving! 
In a gale I have seen the Calshot Spit light vessel almost bury it bow in a big wave and that was in the relatively sheltered Solent. Imagine what it must have been like in exposed areas in the Channel and North Sea. The high bow was designed to keep the water off the deck as much as possible. They didn't have the option of running for shelter.
Trinity House, a bit like the RNLI have their own designs for specialist purposes so especially when the ship started to be built of iron and steel they would not have converted from other types. Like Colin said, they are not designed for speed and in normal use only have to go as fast as the tide!
Tim R