When you have free parameters, you are actually opening the door to a whole family of predictions. You're saying that of this entire family of models, you'll ch

When you have free parameters, you are actually opening the door to a whole family of predictions. You're saying that of this entire family of models, you'll choose the one that best fits the data. Without free parameters, you have to come in with a fully specified model to begin with. Loosely speaking, with an incorrect family of models, there's a lot of wiggle room to find one that still looks quite a lot like your data, while that freedom is not there when making a single specific prediction. There are semi-rigorous ways to take that into account while comparing models https://methodology.psu.edu/node/504 https://methodology.psu.edu/node/504