Yes it is true that BHT won't grow too long, and will retain the characteristics it had at the donor site. A good reason not to use pubic hair, eh!
Well, I've done an enormous amount of research on this... so listen up!
BHT FOR REPAIR PATIENTS
I have seen some incredible results using body hair in hair transplant repair patients. The results don't look undetectable in most cases, although they can be an extremely big improvement for some repair patients (some can be seriously affected by previous botched surgeries from years before - and may have limited donor supply, making the back-of-the-head donor area impossible to use).
Having said this, I have seen some other examples of BHT that look ultimately very detectable . These are typically in cases requiring larger numbers of grafts over a larger area - and NOT refinement style work that I'll mention below...
BHT FOR FEATHERING HAIRLINES
Another point which is MASSIVELY IMPORTANT but which is definitely overlooked by the hair transplant community is the ability for body hair (despite its short length as you point out) being used to feather pre-existing hairline hair transplant work.
One such example is sofarsogood's surgery by Dr Umar, which can be viewed on youtube. This is, by a huge margin, the most impressive and undetectable hair transplant final result that has ever been documented. It is absolutely impossible to tell any work has ever been done. I challenge anyone to disagree. Still, despite this I don't often see it cited as an example of flawless work. It really needs more attention imho. People need to know what is possible.
SOME OTHER POINTS REGARDING BHT
As always, it really depends on your own hair characteristics and the type of work you require. Feathering of hairline work does seem to be the IDEAL application of thigh hair BHT, because it very, very closely matches the shorter and thinner hairs found in the hairline.
Whereas for instance a NW3 to NW1 surgery (which would need hair from various part of the body including perhaps beard hair, chest hair etc) would typically yield a much more detectable, much coarser and pluggier result.
I suppose I don't feel comfortable classifying BHT as simply BHT. There needs to be some further clarification when discussing this kind of work, since body hair varies dramatically in texture and length depending from where on the body it is taken - beard hair is nothing at all like thigh hair, etc.