My experience is very different, but perhaps we live in different parts of the world. There are people in most walks of life who have beards, or drink Guinness, or have longish hair, or who are going bald. Some of them sing, some wear suits; sometimes simultaneously. Others are clean-shaven and prefer other drinks and styles of dress. Many, indeed, are women and do not suffer much from beards or baldness, though their hair may be long. So what?

It is best to avoid stereotyping, which on the whole gets nobody anywhere. I don't see the point of that part of your question, which I assume refers in any case to "singers of traditional songs" rather than "traditional singers"; the two things are not the same.

As for speaking the last part of a song, that has been fairly common practice -in England, and doubtless elsewhere- for well over a century (likely longer, but information on that is scarce). It isn't compulsory, and not all traditional singers did it. It's a way of bringing the singer, and perhaps the audience, back into the here-and-now after the narrative (sometimes highly emotional and involving) is concluded.

Singing with the eyes closed was also something remarked upon frequently by the early 20th century collectors. It might indicate shyness in some cases, or it might be a way of focusing on the song; or both. At all events, it was quite common.

Whether today's revival singers do these things for the same reasons, or because they think they are supposed to, would perhaps depend on how deeply involved in the whole thing they are.