RE: The Piccolo Violin: A forgotten instrument
That is a good point, and some musicians do use that compromise solution.
However, it does have a few drawbacks. The first is that the Piccolo is not exactly a half or a quarter size in all its dimensions. The body (the resonance chamber) is larger than the comparable proportions that you would expect from the fingerboard (and string length). So, by having a different proportion of these two measurements, you already have a different quality of sound.
The second part is that most (of not all) of the smaller sized instruments that are made today are of poor quality compared to a professional standard. Thus, you would have to ask a luthier to craft a high quality smaller instrument. And if you were going to do that, you may as well ask for a copy of the real thing!
Edit: I mixed up the relationship, the body is smaller than the neck would suggest.
Yes, you're right, the small size violins are usually basic instruments designed for young beginners.... :-)