The case for points over time estimates as I understand it, is that humans are not necessarily good at estimating in terms of time. We are good at estimating complexity in reference to other similar things. You can estimate that a new task is more/less/the same complexity as a similar task performed in the past more accurately than how long it will take.
After a while of doing this (as a group, not individually), you can get a velocity that starts to give you a good historical estimate of how long it takes to complete a given point, and use that to have realistic commitments for your work.
Note that one team cannot be compared to another because each group will estimate differently, with one group maybe estimating more conservatively, so their points and velocities will seem bigger and more productive than other groups. This is the reason why management should not use velocity as a performance indicator.
Since you need a history of estimating to get the velocity to accurately plan, this system is unreliable if the team is constantly switching out teammates. At my company we switch up the teams pretty often, so pointing doesn't really work well for us in this case.