No. Although most teeth that have had root canal treatments do need crowns to strengthen the tooth because removing the nerve can leave it brittle, there are plenty of other reasons why you might need a crown.
Dental crowns are often used to strengthen a tooth that has a very large filling that has weakened over time. Crowns can also be used cosmetically to fix a tooth that is misshapen or badly stained and resistant to whitening.
Root canal therapy, which is also referred to as endodontics, is generally needed after an infection develops in the pulp of your tooth. You will usually become aware of this because you will have a toothache that gets progressively worse. Infection often starts because decay in a tooth goes unchecked or because the tooth surface becomes fractured, allowing bacteria into the soft center of the tooth.
Although a root canal sounds scary, it is a simple procedure that not only alleviates your pain but saves your infected tooth from extraction. It is just as easy as getting a run-of-the-mill dental filling.
In many cases, covering a cracked or damaged tooth with a crown prior to an infection developing is sufficient treatment and a root canal is not necessary.