My Elan starts on the button doesn't overheat is comfortable and really usable as well, and it's absolutely bog standard as it came out of the factory in 1967.
Yes, it's the purists's view! But with a slight difference.
I think that Clive is spot on...it depends what you want out of the car. There is no reason why a standard Elan can't be utterly reliable and used as an everyday car. I know a chap who is just coming up to 500,000 miles in his S4, used every day all year round in city and country. However, he maintains it properly to standard servicing intervals. That includes a complete overhaul (rebuild) every 100,000 miles.
Many Elans have never had a proper rebuild, but have been botched and made to go a little bit further until they can be offloaded to the next unsuspecting punter. Their reputation was never that good because service intervals are roughly twice that of a contemporary Ford, so folks didn't bother even when they were only a couple of years old.
So if all you want is for it to start properly, be reliable, comfortable and not overheat don't waste you money...get the car sorted to original specification, but accept that you will have to spend more time and / or money maintaining the car properly.
If you want the car to go faster and handle a little sharper then you could go the Zetec route...or buy a modern Lotus. I doubt that you'd get a Plus 2 Zetec to go round a circuit quite like an Elise, so I don't see the point of that either.
So the only possible reason left for doing it must be...because you want the fun and challenge of doing it! And to a large extent, that's the common thread for all Elan owners, whether you want to make a car the fastest on the track , the best looking or the most original. There's no right or wrong. It may be different if there were only 3 left in the world.
A couple of things to consider. The first is where you're starting from. If you have a sorted Plus 2 with a good chassis and fresh engine, I would sell the car and buy one that isn't as healthy. You can still get a lot of money for a knackered twincam it seems, and you're going to throw the chassis / suspension away anyway.
Second point...You've got ?15,000 to spend on a Plus 2 and you go into a showroom. There are two identical Plus 2 cars there...both mint and the same colour...one's totally original and the other is a Zetec. Which one would you buy?
Just to show I've a balanced view
I am currently restoring a late 130 to original factory spec...lots of new-old-stock, lots of money on paint, engine rebuild etc. I've also recently been offered a Plus 2 which was fitted with a BDA engine from new...big bump on the bonnet, straight through exhaust, and I love it to bits!
It's up to you.
Mark