He didn't have to. If time were unlimited, one could do any number of good deeds, and it would literally not matter how many of them you did, you could always do more... and thus there would be no competition between choices of how to use that time.

You'll note that what he did mention was effort, an entirely different resource, particularly as it applies to humans.

The assumption that not doing something now lets you do more later is false, however, because the time is already passing

This isn't an assumption of Vladmir's, it is yours. What we do know is that spending $10 now is $10 that you can not spend later. More importantly given what we know about how humans spend money, $10 you are spending right now on one (completely useless) charity is $10 you are unlikely to spend within this month on an altruistic act that is, in fact, useful.