Out of curiosity, can you tell me what kind of flour you used? I think you were introduced to the realities of what I will refer to as "pizza death". Once a pizza comes out of the oven, it starts to decline in quality, and fairly quickly. Pizza operators who deliver pizza to their customers know this all too well, and it is not at all uncommon for delivery pizza, especially pizza based on high-gluten flours, to become tough and leathery by the time it reaches the customer. In fact, some operators choose to use a lower protein flour, which is softer than high-gluten flour and less prone to turning tough and leathery.
In a home setting, what I frequently do is place slices of my pizza on my pizza stone as it is cooling down (after I have turned off the oven). The residual heat from the stone keeps the pizza hot and crispy, just like I like it. But if I just let the pizza sit around, it won't be long before it starts to degrade and become leathery. But it usually won't be wet or moist because of moisture being introduced to the bottom of the pizza.