It's not different time preferences. According to time preference theory the insurers have perfect information about the future so they would have taken the change in lifespan induced by GLP-1 into account before it was even invented. The assumption that mistakes are impossible is one of the core foundations of neoclassical economics. In time preference theory the bias towards the present or future is a moral issue that you get beaten over with to enact a just world fallacy.
In liquidity preference theory insurers do not have perfect information so they must make a tradeoff between collecting information and acting on the information they already have. There will be a bias towards the present and the past, because more information is available about the past and present than the future. What's being "discounted" is uncertainty, not time. Hence there is also a general bias towards stability and conservatism (sticking with existing decisions, even if they are bound to become obsolete).
Now let's apply this to the article:
The insurers don't know if you can stick with your weight loss, so they will conservatively deny coverage until they are certain that they know your health/risk profile. According to time preference theory this would never happen since the insurer already knows whether you will succeed at weightloss or not.
In liquidity preference theory insurers do not have perfect information so they must make a tradeoff between collecting information and acting on the information they already have. There will be a bias towards the present and the past, because more information is available about the past and present than the future. What's being "discounted" is uncertainty, not time. Hence there is also a general bias towards stability and conservatism (sticking with existing decisions, even if they are bound to become obsolete).
Now let's apply this to the article:
The insurers don't know if you can stick with your weight loss, so they will conservatively deny coverage until they are certain that they know your health/risk profile. According to time preference theory this would never happen since the insurer already knows whether you will succeed at weightloss or not.