Not all statistical procedures split in to training/testing data, also called "cross-validation" (although the entire procedure involves a little more than that).
Rather, this is a technique that specifically is used to estimate out-of-sample error; i.e. how well will your model predict new outcomes using a new dataset? This becomes a very important issue when you have, for example, a very large number of predictors relative to the number of samples in your dataset. In such cases, it is really easy to build a model with great in-sample error but terrible out of sample error (called "over fitting"). In the cases where you have both a large number of predictors and a large number of samples, cross-validation is a necessary tool to help assess how well the model will behave when predicting on new data. It's also an important tool when choosing between competing predictive models.
On another note, cross-validation is almost always just used when trying to build a predictive model. In general, it is not very helpful for models when you are trying to estimate the effect of some treatment. For example, if you are comparing the distribution of tensile strength between materials A and B ("treatment" being material type), cross validation will not be necessary; while we do hope that our estimate of treatment effect generalizes out of sample, for most problems classic statistical theory can answer this (i.e. "standard errors" of estimates) more precisely than cross-validation. Unfortunately, classical statistical methodology1 for standard errors doesn't hold up in the case of overfitting. Cross-validation often does much better in that case.
On the other hand, if you are trying to predict when a material will break based on 10,000 measured variables that you throw into some machine learning model based on 100,000 observations, you'll have a lot of trouble building a great model without cross validation!
I'm guessing in a lot of the physics experiments done, you are generally interested in estimation of effects. In those cases, there is very little need for cross-validation.
1One could argue that Bayesian methods with informative priors are a classical statistical methodology that addresses overfitting. But that's another discussion.
Side note: while cross-validation first appeared in the statistics literature, and is definitely used by people who call themselves statisticians, it's become a fundamental required tool in the machine learning community. Lots of stats models will work well without the use of cross-validation, but almost all models that are considered "machine learning predictive models" need cross-validation, as they often require selection of tuning parameters, which is almost impossible to do without cross-validation.