James,
Whether sailing without an engine is wise or not, depends of many factors.
Work and family situation:
If you don’t have a fixed work schedule, you are quite free to leave and return as the wind and tide allows you. Quite the opposite would be if you need to be home to go to work, or for the children to get to school in time: That would suggest; fit a reliable, fairly powerful engine.
Preferred harbours.
If you frequently use marina-type harbours, you will need some sort of engine, not necessarily so powerful, but reliable and easy to operate for close manoeuvring.
Staying off a lee shore.
Your Elisabethan 31 is probably more weatherly than most and should let you climb away from a lee shore in quite rough conditions. If the wind is too light and the tide too strong, you’d better have a good anchor ready. However, a quick-starting engine is seriously nice to have for coastal cruising: If something goes wrong in the rig, one has little time to sort it out before hitting the shore. A reliable engine, even a not so strong one, raises the safety level. If the engine is not strong enough to push you straight against a strong wind, you can still tack your way upwind under engine, with such a good hull.
Long distance cruising.
I bet those who cross oceans, sail a much larger part of the distance than most coastal sailors do (with or without a work schedule). I guess I would still have a small diesel on a 5-ton boat like yours, partly to sneak over wide calm spots at low speed. To minimise complications (..and keep you from getting a “12Volt neurosis”... ), I strongly suggest you choose an engine which can be hand-started. This frees you from bothering with all these battery and charging backups - and backups on the backups: No fear of being stuck on a “black ship”.
Anchoring.
A good anchoring setup will help keeping you safe and free from using marinas often. However, your boat is over 5 tons. That means you have to pull or winch up a quite big hook. My guess is that, after a few years, an electric capstan or a regular anchor winch will, little by little, have moved upwards on your wish-list. Then, somehow you need to charge the battery. Don’t ask me if solar panels are enough for that, I don’t know.
Sooo,
I think I in most cases would suggest fitting an engine. The ability to hand-crank it in a pinch saves you, as said, from the usual electric complexity and confusion connected to most diesel engine installations.
Arne