Why is it good scientific practice to 'build' a 'control Earth' from models, and where else do we 'build' controls?
It's true that, usually, when data is collected in an experiment scientists have a control, and very often not having a control results in a flawed experiment - that is, an experiment from which less conclusions can be drawn.

Experiments are a very efficient way to gather high quality data, but in some fields they might even be impossible. However, experiments aren't the only way to get knowledge and they aren't mandatory to make science.

In some fields experiments are quite easy and therefore most research is based in experiments. For example, it's usually easy for chemist to test the way substances react by making experiments.

In other fields some questions can't be resolved by direct experiments due to practical or ethical reasons. In a known textbook example, sociologists are interested in what circumstances cause suicide rates to rise or drop, but ethics prevents them from performing an experiment by submitting a sample of people to circumstances supposed to induce suicide and compare suicide rate of this sample with suicide rate in a control sample. Therefore, sociologist need to draw conclusions from observational data - that is, observing real population under natural circumstances they can't adjust - or from experiments of related phenomena that can be performed without ethical concerns.

We in Earth sciences face a similar problem: some experiments can't be done because of scale or just because we just have an only Earth. For example, how do we know that rivers cause deltas? Ideally, we'd like to do an experiment by selecting several coast tracts, putting rivers in a randomly chosen sample of them, waiting a few millions of years and comparing evolution of the coast tracts with and without rivers. We can't do this experiment, but it doesn't prevent geologists to have learned a lot about deltas, because we have a lot of data from observation of naturally occurring deltas, from small scale experiments, and from study of auxiliary sciences (physics, hydraulics, etc.).

Climate is similar to deltas. Just as we can experiment with setting and removing rivers, we can't change CO2 levels of the whole atmosphere to measure what happens, but we can observe what actually happens, search for geological register of what happened in the past, do a lot of small scale experiments, and use our knowledge of basic sciences and draw conclusions about climate evolution from them.

Clearly, interpretation of that data is not as straightforward as data from a big experiment would be, but it is still possible and useful. In fact, it's the way most of current knowledge in many fields has been built.

All that without needing a random sample of Earths nor a control Earth.