But a more important reason to solo early in pilot training is so that I can assist them in the fledging process while we still have plenty of dual time left. In my experience, teaching decision making is the hardest part of pilot training, and the best way I've found to do that is by reviewing their solo flights and providing scenario-based training on following dual flights. Additionally, by having full dual lessons mixed with full solo lessons in stage 2 & 3 it allows me the opportunity to review the habits they are developing during their solo flights, and work with them on decision making. Decision making is the most important skill, but also the hardest to test and evaluate. It's easy to make decisions well enough to pass a check-ride, but that doesn't necessarily equate to having the skills required for real life.
YMMV.