The reasons people get in to building are as varied as the individuals, but the main one is; "because they want to". After that, it gets more personal.
But generally with these military arms, they build them because originals in shooting condition are far too scarce, valuable, (or of questionable integrity) to shoot safely or wisely. Those (commercial companies) that make reproductions of those (military) guns tend to not be making arms that are "correct" creations when viewed side by side with the originals. The only way to get a "correct" one is to either build it yourself, or contact a custom builder to have THEM make it for you. Of course, if you can live with the variations from the originals that the current manufacturers do, then by all means go with one of them. It really all depends on what is the most important to you.
When you are getting in to AWI period, and Golden Age stuff then you are dealing with arms that were made (in the period) in smallish one-off type of shops, and they were all hand made, one at a time. Very few of them were done the same way time and again (with a few exceptions, like John Armstrong). Parts tended to not be standardized, so they generally do not interchange without modification to them. In those days, the focus was on having a functioning firearm, with a little art on it. These days (for many) the focus is on the art to be attached to a functioning firearm.
A lot of recreational builders just like to tinker with mechanical stuff, and are comfortable working with wood and metal. The carving and engraving aspects let them express themselves creatively, and when they are done, have a family heirloom piece of which they are justifiably proud. For many, just making one is not enough. (And you really can't ever have enough guns.) They seek to improve themselves through subsequent builds. Most builders start out with a rather plain and unadorned gun, built from a kit or pre-carved parts set, and then move on to greater personal challenges, adding things like building from a blank, carving, engraving etc. By the time they're on their 5th -10th gun, most have gotten pretty good at what they do, and some even move in to the contract build "business", though when they do the math on their wages, and on a "per hour basis", they really don't make much more than minimum wage at it.
So that brings it around full circle. Most builders are builders because they want to, and they want to make something that they themselves are happy to say "I built that".