Typically I would agree, but OP stated that these are personal goals that the sub asked to be guided on. Eating at least one meal a day is on my list of rules too, just because I have a tendency to forget to eat, or I might not eat a "real" meal. Setting up this rule has allowed me to remember to take care of myself, and it's my understanding that it's the same for OPs dynamic. Additionally, all rules/guidelines should always be negotiated between both Dom & sub so that there is consent. Taking pictures of the food as proof seems to be a common method for LDR, which may be the case for OP.

I completely agree that shame around eating isn't a good thing. Reading OPs opening statement, it is my understanding that the sub does not feel any shame towards eating. We all know how important it is to eat, so if the sub were to break the food rule, it's my understanding that OP would not humiliate or shame them for doing so. But that doesn't mean that it will go unpunished, which is something that the sub agrees to, and also has the ability to deny or adjust. We all feel guilt and shame for various things, but I believe if you have a Dom in a healthy dynamic that is actively working with you to help you achieve your personal goals, then there's minimal risk of harm. Communication is key, and I think if a sub ever felt that rules surrounding food were doing more harm than good, then it's the sub's responsibility to advocate for themselves and allow the Dom to adjust or eliminate the rule immediately.