Depending on the capacitors' technology, their failure modes can include shorts. Which may destroy much more expensive and unobtainium circuitry. So waiting for a failure is not always the best option either.
AFAIK, particularly the following: film capacitors, tantalum and ceramic. Ceramic caps failures being often due to mechanical stress, especially the SMD ones.
The electrolytic ones are usually more going either open, have increased leakage or increased ESR when drying up. That may also lead to other failures over time due to excessive heating/ripple, but bad electrolytics are usually easier to spot visually, as they are often bulged and/or leaking.