Hot-melt glue guns are very useful in a range of crafts, for example sticking items together where there is no joint, such as paper flowers onto a piece of coloured cardboard. In woodworking, hot-melt glue is sometimes used to temporarily hold together parts when working on them if they are awkward to hold onto. In such cases, once a piece is finished being worked on, the hot-melt glue is removed.
But to your question regarding using hot-melt glue to re-glue the top rail of a chair - it is not suitable for at least three reasons. First, hot-melt glue is very thick (high viscosity) and coupled with having to work fast before the glue cools, it is near impossible to sufficiently close the gap between the parts. Second, the glue tends to be messy to apply and difficult to tidy-up. Finally, to make a good repair, the old hot-melt glue normally has to be carved away to clean wood before a proper re-gluing with PVA or epoxy can be made. PVA is the pre-eminent glue used in woodworking. While there are many other types of glue used to make or restore furniture: hide, epoxy, CA, wheat, F-2, etc, PVA (wherever possible), is the preferred glue to use in making or repairing wooden furniture. Heres my favourite: http://www.titebond.com/product/glues/e8d40b45-0ab3-49f7-8a9c-b53970f736af