This is just false. Time cannot be your most precious resource, because there are many, many ways to push the likelihood of you dying tomorrow, next year, or next decade down considerably from where it is. Exercising, for example, or reaching a healthy weight, or quitting recreational substances like alcohol or opioids. Yet in reality we see a great many people who refuse to do any of these things, and statistically end up with less time because of it. Empirically speaking this is very strong evidence against time's claim to ultimate value.
It's true that there seems to be a maximum amount of time our unaugmented wetware can provide us, but something being finite does not make it the most important thing you have. I have a finite amount of money in my pocket, yet money isn't my terminal goal.