The Department of State tells us:
Additional Documentation May Be Required
Review the instructions for how to apply for a visa on the website of the U.S. Embassy or Consulate where you will apply. Additional documents may be requested to establish if you are qualified. For example, additional requested documents may include evidence of:
- The purpose of your trip,
- Your intent to depart the United States after your trip, and/or
- Your ability to pay all costs of the trip.
Evidence of your employment and/or your family ties may be sufficient to show the purpose of your trip and your intent to return to your home country. If you cannot cover all the costs for your trip, you may show evidence that another person will cover some or all costs for your trip.
Note: Visa applicants must qualify on the basis of the applicant's residence and ties abroad, rather than assurances from U.S. family and friends. A letter of invitation or Affidavit of Support is not needed to apply for a visitor visa. If you choose to bring a letter of invitation or Affidavit of Support to your interview, please remember it is not one of the factors used in determining whether to issue or deny the visa.
So yes, you would bring this at the time of the interview, but the chances this will change the outcome are low, and it is only useful to justify the fact that someone else is going to bear the costs of the trip (lodging, food). Ideally the application should stand on its own merits. A letter of invitation will not in any way change positively the evaluation of whether the applicant has enough ties to their home country (quite the opposite, really).
The site of the US embassy in the Dominican Republic goes further:
Do I need an invitation from an U.S. citizen or someone in the U.S. in order to qualify for a tourist visa?
We understand the wish of U.S. citizens and residents to have family members visit the United States, and to send letters of invitation. An invitation is not required and cannot guarantee visa issuance. In fact, there are no required documents for tourist/business visa applications. Visa applicants must qualify for the visa according to their own circumstances, not on the basis of a sponsor’s assurance. Based on the application and interview, a consular officer determines whether or not the applicant qualifies for a visa.
In order to qualify for a visa for business or pleasure to the United States, each applicant must demonstrate that they qualify based on U.S. immigration law and:
- They have a residence in a foreign country to which they will return to after their temporary visit;
- Intend to enter the United States for a period of a specifically limited duration; and
- Will go to the United States to engage in legitimate activities relating to business or pleasure.
The first requirement, proof of residence, is generally determined by evaluating an applicant’s ties to their country. Examples of ties are employment, property ownership, university studies, and/or family. Each applicant’s ties are unique and are considered individually by a consular officer.
For tourist/business visas, the most commonly applied for visa class, applicants must be able to demonstrate to the satisfaction of the consular officer that their travel plans fall within the parameters of the requested visa class – limited travel for pleasure or business (but not employment) of short durations. Applicants must also be able to demonstrate that they will depart the United States in a timely manner to return to their residence abroad.
In addition to demonstrating strong ties, an individual must show that he or she will use the visa appropriately. This means convincing the consular officer that all activities in which the applicant expects to engage in while in the United States are legal and consistent with the requested visa class. This is the case regardless of the applicant’s financial situation or ties abroad.
Basically, they are clearly contradicting your assumption that
an invitation letter absolutely helps
And say the exact opposite: it is useless in asserting any of the 3 points they matter, which essentially come down to ties to your home country, ties to your home country and ties to your home country.