Letters of recommendation are an essential aspect of the path to residency. A successful candidate has strong letters of recommendation from respected individuals who offer clear, unbiased information while still painting the candidate in the best light. As a candidate for residency, you should be making sure you highlight your strengths on all fronts. A good way to ensure this is by exercising your right to review your letters of recommendation.
Why would a candidate ever waive their rights to review their letters?
Letters of recommendation sent directly from the writer to a residency program may be considered to have more weight due to the assumed unbiased nature of the content. If the writer knows that the candidate will never read the letter, s/he may be more inclined to speak truthfully. Because of this assumption of honesty, a letter that has been reviewed by the candidate may be assumed to contain biased information. In this instance, a candidate may choose to waive their right to review the letter, and instead send it straight to the program. This leaves the candidate with no way to confirm the focus of information, the level of praise, or the accuracy of details written in the letter; all of this information is crucial to residency programs’ consideration of a candidate.
How can reviewing your letters benefit you?
If you are prepared to explain your reasoning for retaining your right to review your letters, you can have more control over the way residency programs perceive you as a candidate. The following points highlight the advantages of reviewing your letters of recommendation:

You can be seen as a moral individual concerned with exercising your civil rights. You take responsibility seriously, and you value self-presentation. These are good professional qualities.
You can correct any factual errors made. This allows you to avoid any confusion down the road and to be sure that programs are receiving accurate information about you.
You can understand the focus of each letter. This is extremely helpful in determining which letters to send to which programs. If a Head of Surgery writes a letter praising your skills in Internal Medicine, you should send that letter to Internal Medicine programs instead of Surgical programs. Having this knowledge helps to emphasize your compatibility with specific programs.
You can get a sense of what information the program has already received about you. This is crucial for interview preparation. By having a sense of what they already know, you can efficiently prepare to highlight the qualities, information, and skills that would best supplement what was presented in your letter.
You can stop stressing about whether the letter is favorable enough. You can know exactly what has been written about you, and determine whether the presented image of you in the letter is beneficial or not.
You can decide not to send an unfavorable letter. This, obviously, is extremely helpful; if a letter does not paint you in the most positive light possible, you can choose to make sure a program never receives it.

Letters of recommendation are all about having reputable sources vouch for you in your journey to residency. It is crucial that you put your best foot forward, and the most effective way to do that, regarding letters of recommendation, is to retain your right to review them.

Sources: https://www.acmedical.org/services/letter-of-recommendation/access/, https://blog.matcharesident.com/guide-medical-residency-letters-of-recommendation/