The notion of using holly and elder for a cheap coffin makes little sense to me. Holly wasn't a commonplace carpentry material. As a slow-growing hardwood it had special uses such as ornamental work, inlays and some furniture so it was not the sort of timber you'd use for a cheap coffin. Elder has a soft core which suggests it isn't suitable for such construction work. It is more often associated with pipes and chanters. Or magic wands, if you're into Harry Potter.

Both holly and elder trees were supposed to provide protection from evil spirits and witches. Holly also had associations with fertility beliefs. Elder was supposedly "feared by the devil".

Although it's purely supposition on my part, it appeals more to me that elder and holly boards are sought for these apotropaic protective qualities, especially if we are to accept the "noble enchanter" theory of what the song is about.

The folklore of trees is very convoluted and it's possible to get a wide range of interpretations if you keep browsing. One site I visited said another name for Elder was "witchwood" but that name can also be used in reference to the Rowan tree and (American) Mountain Ash. One use of witchwood that caught my eye (apart from warding off witches) was to "keep the unhappy dead in their grave". Yes that's all pretty tenuous but it does fit nicely with the story line of the song!

I rather like the fact that we will never know. Art and literature (including oral traditions) should stimulate our imaginations. It's quite okay for us to take away different interpretations of this song. It's a great and mysterious song that's worth keeping alive.