I am told that one of the main benefits of Survival Analysis models are their ability to handle Censored Data. This is in contrast to standard regression models that are unable to do so.
For example, suppose researchers in a medical study are interested in knowing if a certain drug is able to prolong the life of patients with a certain disease : in this medical study, a patient dying is considered as the "event. Suppose one of the patients has to move to a new country 5 years after the study has started and we are no longer able to collect data on this patient. We know that the patient survived for at least 5 years. In a classical regression model, the data for this patient would be considered as "incomplete" and we would not be able to use the data for this patient in the model. However, a Survival Analysis model would let us use to the "complete part of the incomplete data" belonging to this patient - thus allowing our model to profit from potentially useful information that would have been otherwise discarded by a standard regression model. In the context of Survival Analysis, this particular patient would be labelled as "Censored".
I am interested in the following (obvious) question: Suppose we have a dataset that contains no Censored Data - for the purpose of a simulation, we decide to randomly "censor" the data belonging to some of the patients. Can we somehow show that estimates from Survival Models (e.g. Kaplan-Meier, AFT, Cox PH) would be "better" on the same dataset when there is less censoring compared to more censoring? (e.g. one dataset has no censoring, one dataset has 5% random censoring, one dataset has 10% random censoring - we fit Survival Models to all 3 datasets and compare the quality of the estimates)
I am aware that Survival Models do not require there to be Censoring in the dataset, and I am also aware that higher levels of Censoring are considered undesirable for Survival Analysis models - but is there some mathematical proof that shows the "decline" in the estimates provided by Survival Analysis models when higher levels of Censoring are present?