You don’t need to mandate it, heaps of people who are obese or overweight are eager to take it, because they are sick of being this way, worried about the long-term health risks, feel the societal sigma, etc. For many such people who currently don’t, the big reason is not that they don’t want to, it is that their insurance doesn’t cover it and they can’t afford the $$$ of paying for it uninsured-but as patents expire the price is going to come down. Other people don’t like injecting themselves, but oral formulations are becoming available
COVID was different because being a transmissible disease, there was a strong motivation to try to maximise the percent of the population immunised. With GLP-1 agonists, if you made them freely available, likely over >50% of eligible patients would take them voluntarily, which would result in massive long-term cost savings from lifestyle diseases, even considering the continued costs from the other 50% who will refuse. And insurers may even give discounts to those who take GLP-1s (if permitted by regulators)
GLP-1s are probably going to have the unintended side effect of increasing weight stigma - already obesity skews poor, once most of the well-off obese people cure their obesity with GLP-1s it is going to skew even more poor. I can foresee a cycle in which GLP-1s increase weight stigma which pushes more people into taking them which then increases weight stigma even more, which could drive up their adoption even further