I have been spinning for a while and just learned to weave using a Rigid Heddle loom. I was told that I couldn't use my handspun on this loom. But I'm not sure why. And I was also told that this wasn't really weaving, but a child's play toy.
I would have to completely disagree with your informants about the rigid heddle loom. I think that the rigid heddle loom can provide a great deal of pleasure for handspinners to use their handspun. Here are several reasons why I like the the simple RH loom.
1. Usually handspuns show off best in a simple weave structure. The RH loom does tabby best.
2. It is economical, since the thrums are very short. It is reasonable to warp up single projects. I hate to waste great amounts of my handspun on loom waste.
3. It is a gentle loom for fragile yarns.
4. You can use a variety of textured yarns in the "slots" and smooth yarns in the holes. Even fuzzy bouclé mohair yarns in the "slots" work great.
5. Simple warp floats can be accomplished with a stick behind the heddle. The stick can remain in place the whole time, by pushing it back on the warp beam. Then just slid the stick up to the heddle when the floats are desirecd.
For the record, in 1985, the handspun wool skirt that won the National Make it Yourself With Wool contest was mine and was woven on my 32 inch wide rigid heddle loom. This skirt was woven with all singles spun yarns.
I always liken the rigid heddle to a guitar, a toy in some hands but truly an instrument of quality when learned and treated with respect. Besides it's portability, and low cost are important assets.
True it doesnot do everything well, it is not useful for twills, or long yardage. But don't discount it completely.