They're not perfect (nothing is), but they're actually pretty good. Every task has to be completable within a sprint. If it's not, you break it down until you have a part that you expect is. Everyone has to unanimously agree on how many points a particular story (task) is worth. The process of coming to unanimous agreement is the difficult part, and where the real value lies. Someone says "3 points", and someone points out they haven't thought about how it will require X, Y, and Z. Someone else says "40 points" and they're asked to explain and it turns out they misunderstood the feature entirely. After somewhere from 2 to 20 minutes, everyone has tried to think about all the gotchas and all the ways it might be done more easily, and you come up with an estimate. History tells you how many points you usually deliver per sprint, and after a few months the team usually gets pretty accurate to within +/- 10% or so, since underestimation on one story gets balanced by overestimation on another.
It's not magic. It prevents you from estimating things longer than a sprint, because it assumes that's impossible. But it does ensure that you're constantly delivering value at a steady pace, and that you revisit the cost/benefit tradeoff of each new piece of work at every sprint, so you're not blindsided by everything being 10x or 20x slower than expected after 3 or 6 months.
Sorry if it comes through as rude, but this is how I keep repeatedly being told story points work.
If you look at all those properties together, story points are completely useless.
The only moment time it makes sense is when you have a SHARED understanding of the smallest point AND you can translate it to time. When you do that, story points are useful. Also, they become time, so there is no reason to use points.
Literally none of that is anything I've ever encountered on any team.
They're not specific to a person, they're to a team.
They have nothing to do with the smallest task ever faced.
They are obviously for summing and are obviously units.
They effectively get translated into time in the sense that the team has a history of delivering an average of n points per e.g. 2 weeks.
Here are literally the top two Google results for "story points" and they both seem to align entirely with what I said:
https://www.atlassian.com/agile/project-management/estimatio...
https://www.mountaingoatsoftware.com/blog/what-are-story-poi...
I don't doubt that what you're describing as story points is something somebody told you. I'm just telling you that their definition was highly idiosyncratic and extremely non-standard. When discussing these things, using the standard definitions is helpful.