NOTATIO

By chance, I've been embroiled in two discussion on different forums about lyrics extension lines. One was: "are they necessary? What purpose do they serve and would anyone care if they weren't there?"
The other one seemed to advocate a creeping modern tendency to draw them across the length of the final notehead, to some arbitrary finishing point (possibly along the same lines as putting consonants 'where they sound' rather than where they are helpful).

So I thought for a bit about what extension lines are for, in my opinion.

With one syllable to one notehead, the singer sings each syllable in turn, 'closing' it with final consonants or vowel changes at the end of the notehead's duration.

An extension line tells the singer NOT to close the syllable at the end of the current notehead, but to keep the vowel to the next or final notehead. The line is essentially a kind of ligature from the syllable to the notehead.

They are perhaps most useful in melismatic passages that include rests: the singer knows that the syllable continues beyond the rest.
Imagine some music with one syllable on one note, followed by many bars' rest. Then a new note, without any syllable. The singer would have closed the syllable and then is unsure what to do about this new note without a syllable.

Now imagine the two notes next to each other, without any rests. The music is the same: one syllable to one note, then a note without a lyric.

Obviously, you have to sing something, so you probably will continue. But that's not what's written. An extension line confirms that the second note is a continuation of the syllable. Its effect maybe subliminal, but is still helpful.

The other issue is adding extension lines where the are not required. I've seen a score recently with extensions on single notes, floating out to some point further in the bar!! An extension line should connect TO something, as a tie or slur does.

I realised a few more things:

Extension lines help at system breaks or page turns to show that the syllable continues round the corner.

Much of the above is true for hyphens as well, but of course you can't use those on the last or only syllable of a word. Hyphens link one syllable to another syllable: an extension line links one syllable to another note (or more).

It might be argued that slurs can be used to convey the same information. Sometimes, yes, though not all vocal music has melismatic slurs, and slurs have other uses. When used in this way, slurs and extensions are perhaps a pair of symbols, slurs on the notation proper and extensions on the textual part.

In short: the answer is Yes, extensions are necessary and useful; and you would notice if they weren't there. You'd still be able to cope, but perhaps a little more hesitant, particularly when sight-reading.