I'll open by quoting the definition from the Wikipedia entry on RCTs:
“A randomized controlled trial (or randomized control trial; RCT) is a form of scientific experiment used to control factors not under direct experimental control. Examples of RCTs are clinical trials that compare the effects of drugs, surgical techniques, medical devices, diagnostic procedures, diets or other medical treatments.” —
When used appropriately, they are an important tool in research. But I must emphasise the when used appropriately. The analysis uses mathematical techniques from statistics which make various assumptions, and it is important to ensure that those assumptions hold, as is the case with any application of mathematical techniques. For example, if a statistical technique assumes that a sample is representative, then in order to apply said technique, one must ensure that their sample is representative, rather than just blindly assuming it is, or assuming it is because you see no other way to analyse your data.