I wonder why this should even be any kind of problem at all. I started learning the violin (although I already had fairly extensive musical knoweledge at the time) at 52. If the teacher has too many hesitations, just ask the next one. And besides, teachers know that our money is probably as good as a seven-year-old's.
Interesting, I never considered that the teacher would think that way but it does make sense. Believe it or not I'm 40 and learning for the first time, when I was a child I wasn't really ready to take on an instrument but now I finally am. I am hoping that even though it takes a lifetime to learn that in the next 20 years I can become competent. I have heard that adult bodies don't quite do it, I guess I am fortunate in being tall with long arms and fingers that that doesn't seem to be an issue for me.
Something I have noticed as well is that many children who start the violin usually give up within a year but adults seem to persist with it because it's what they really want to do, they are making a choice where many children are being told to play by the parents. So is it worse for adults to take on an instrument or for many children to give up so quickly? It's an interesting discussion I've seen before and there are many views, I don't think one general view fits all people.
Oh and even though I'm 40 and playing the violin for the first year I have a wife as well!!!
I have been teaching for over 18 years and have taught a few adults in that time. Adults, unlike some children, are very motivatated to learn and practise. There are only two main differences between adult learners and children: firstly, adults ask a lot more questions and are more interested in the "whys & wherefores" of technique and secondly, they remember much more of what you tell them! Adult learners are very committed to practising also. So, no, I don't hate teaching adults. In fact, it's more the opposite.
In fact, my favorite kind of students are "kids" aged 50 or older :) LOL
Seriously though I do like working with adult students. They are more of a challenge in some ways, but less challenging in social ways. My preference is to work with adults. I've been teaching professionally since 1986.