Always remember that insurance companies are not in business to help you. They are there to collect your premium dollars and not pay claims.
Having said that, I think it is important to have. If you have the cash flow for it, buy it. I bought mine when I was finishing my OMS residency. I have a good friend with whom I grew up who was an agent for a well-known company, and he told me everything about it. Of course, he sold me mine when I was young. You cannot now buy what I have.
For disability insurance, be sure that it covers you for your specific job..."clinical dentistry", etc. If you lose a hand, the insurance company will do everything it can legally to avoid paying. For example, if your undergraduate degree is a B.S. in biology, they might say you can get a job teaching biology, and then deny your claim unless the job description is specific. Ask if you can change the job description as you advance (e.g., to a pediatric dentist).
Also, know that if you pay your disability insurance with post-tax dollars, the benefits are tax-free (at least for now). If you get disability insurance as a benefit from a job, then that is pre-tax, and you will have to pay tax if you collect the benefit.
Moreover, you are allowed only so much disability insurance. There is a finite value that you can receive. So consider that when buying it. I declined such insurance with a job I had once because it would cut into the amount I already had.
Did I say insurance companies will do everything they can legally to avoid paying a claim?