You are incorrect. GLP-1s modify food desires as well. “Will power” is merely hormone levels in this regard.

https://jamanetwork.com/journals/jamanetworkopen/fullarticle...

> Glucagon-like peptide-1 receptor agonists (GLP-1RAs) are increasingly used for type 2 diabetes and obesity treatment. Their effects on appetite and satiety are well established, but less is known about their associations with food purchases. Case reports and small observational studies suggest that GLP-1RA initiation is associated with altered preferences from highly processed, energy-dense products to minimally processed foods. We examined whether initiation of GLP-1RAs for treatment was associated with changes in nutritional quality and processing level of supermarket purchases.

> Changes in purchasing patterns after GLP-1RA initiation were seen across most nutrient categories. Opposed to comparisons, after the first prescription, participants purchased fewer calories, sugars, saturated fats, and carbohydrates, alongside modestly more protein. The share of ultraprocessed foods also decreased. Although modest at the individual level, these changes may accumulate at the population level, particularly given increasing GLP-1RA use.