Having the delete address functionality in the checkout process is fine, as long as it is accessible elsewhere. Consider the frequency of checkouts by the user and whether this will add or remove friction each time the user repeats a purchase.
If a user is a frequent shopper at the site, and they are aware that full address management is possible during the checkout process, they are more likely to engage with the shopping-related activities first, even if they are at a different location. Anticipating anxiety should be the top priority, as it is the most significant cause of friction and revenue loss.
Users are anxious if they believe they might lose their shopping cart over navigating elsewhere to update an address. This conflict is magnified on mobile.
Users are anxious if they believe there's a chance they sent the order to the wrong address, deleting it eliminates the error possibility. For example, they had purchased while traveling for work, and know they entered the hotel address, however, there is no incentive to keep this address. As the amount of addresses increases, the possibility of error is more significant.
While avoiding anxiety would also influence the decision of using a form vs. modal, the main concern, in this case, is reducing cognitive load for the user. The cognitive load imposed on a user during checkout is significantly reduced if the context remains the same during the entire process, so I'd advise against the modal. This decision not only helps to achieve the goal (purchase) but it will also free the user from selective attention mode and make them more likely to engage with other aspects of the site, like special promotions, or post-purchase actions.
I don't know what you mean by references. My understanding of this subject comes from studying user behavior and decision making processes, I'd look for research produced on those topics.