While ship design isnt strictly necessary, it definitely gives you the edge in all areas of the game.
For a start, you really want to upgrade your coloniser/constructors to make use of new engine designs. You can design highly specialised ships such as mass sensor arrays to act as border patrols. In fact, the possibilities in ship design really make this game special - and that's really without worrying if your ships look cool.
Remember, if you take the time to design a ship and like the outcome, dont put any engines, weapons, defenses or other modules on it.... just save it as a (Class name) with the description as "barebones fighter" or whatever. Then you can upgrade it from the shipyard, whack new techs on it and save it as MK1 (Class Name).... then the next time you have some new techs, do the same again and call it MK2 (Class Name).
In the next game with that race, these will natually unlock for you as you research new techs. Thus, the inital time you invest pays off in the long term - you have MUCH better ships than the stock ones with a highly specialised task and you dont even need to do any more design as they just appear ready to be built with new tech discoveries.
I honestly dont know how anyone could play the game without at least dabbling in ship design!