Based on what you said, can one say that this is really a potential infinity, since there is no point you can indicate and say that there are infinitely many like it, and what we have here is a mathematical way of looking at the structure of a continuous line, not that infinitely many concrete points really “exist.”

I didn’t understand the claim. There are infinitely many like it in the potential sense.

That’s exactly the point: there’s no problem with there being infinitely many such points potentially, but they do not really exist concretely. (Because there is no point you can indicate and say that there are infinitely many like it.)

I lost you. You can point to any point and say that there are infinitely many like it. It’s only the term “infinite” that is interpreted potentially.

I didn’t fully understand you, so I’ll try again from the beginning and write it more clearly.
I want to argue that there is no actual realization of a concrete infinity here, because you can’t point to any point (with any size whatsoever) and say that it exists infinitely many times (because we do not have infinite area); infinitely many points exist only in our minds through a way of looking at the structure of a line, but those infinitely many points do not really exist.
(That is, you can think of infinitely many points by means of a mathematical sequence, but you cannot actually point to infinitely many points, and therefore they also do not really exist—just like in an ordinary number sequence.)

I’m not sure you understand what you wrote. What does it mean for a point to exist infinitely many times? Why, if it exists infinitely many times (whatever that means), should it occupy infinite area (you probably mean length, and even that is of course not true).

We can relate to a given line as infinitely many points only in the form of a mathematical sequence, but we can never project that sequence onto reality.
What I meant was that no matter which point you choose from the sequence, it does not exist infinitely many times (because any nonzero size multiplied by infinity would equal infinity, while the length of the line is not infinite).
This is seemingly exactly the difference between a potential infinity and a concrete infinity: you can talk about it mathematically, but infinity has no actual realization.

This has nothing to do with concrete or potential. A collection of infinitely many points does not yield infinite length, and in fact yields no length at all. Beyond a collection of points, you also need the property of density in order to create a continuum (and in Leibnizian elementary-school language, the continuum is made of differentials, not of points). A differential is a line whose length is 0 (tending to 0), whereas a point is something with no length at all. It’s like the difference between a blind person who does not see and someone who sees only black (a neutral appearance).

Okay, so the term “points” was mistaken; instead, one could replace the word “points” with “segments.” I didn’t see a rejection of the actual argument—why does it have nothing to do with potential and concrete?
But now I understand your point that points are not necessarily entities that exist. Only now I’m asking the same question not about points (which have no length at all) but about segments (which do have some length).

There is no fundamental difference between segments and points. Take N segments, each of length 1/N, and the total length is 1. Now let N be infinite. The total length is still 1.
I think we’ve exhausted this.