No one seems to be able to decide whether this question is worth answering or not, I will put one down just to bring closure, summarizing some of the discussion in the comments. I think that the question merits answering because the genetics community honestly hasn't done a good job of messaging on this topic.
It's a little involved, so I'll break it into parts. It's a bit long, so for a tl;dr you can skip to the conclusions.
what does "less than 1% different" mean?
First, it's important to know what the widely cited statistic of ~0.1% difference between the average pair of humans means. It means that, of alignable sequence, if you look at ~1000 bp, approximately 1 bp will be different. As a point of comparison, most great apes (including humans) differ from each other by 1-2% by this measure.
However, not all of the human genome is thus "alignable" even between two humans. When I say "alignable", what I mean is that I can take a snippets of two sequences (say, a 100 bp region) and 1) confidently determine that the area is the same on the two genomes, and 2) we can actually associate specific ACGT with each other between the two sequence. Such a 100bp snippet is then "alignable" with regard to the two genomes.
When sequence is not alignable, that usually means that it shows redundancy in the genome, which is to say that it is present in more than one copy, or a similar enough sequence is present that my confidence in a unique placement is low.
In other words, the 0.1% statistic is actually based on the subset of the genome where we can perform confident comparisons. If this minority of the genome were representative, this would not be an issue. But the alignable portion of the genome is highly non-representative, as it contains most of the genes that we care so much about, and none of the big important structural pieces like telomeres and centromeres. This non-alignable region is in part so hard to analyze because it has a much higher mutation rate than the rest of the genome; in other words, we expect the non-alignable regions to be more variable than the alignable regions. Probably much of the genetic variation among humans occurs in these regions.
So the 0.1% estimate is a significant underestimate of divergence. It is nonetheless a useful heuristic for thinking about relative degrees of divergence.
Why don't humans vary genetically more than they do?
This is, I believe, the heart of your question. Whether the true difference is 0.1%, or 1%, or 5%, one could ask why it isn't 30% instead, as you do in your comment. It seems that you are at least somewhat interested in this from an adaptationist point of view, namely that one can imagine that all that extra variation could be helpful in making humans "better", however we happen to define "better" (faster, stronger, smarter, disease-resistant).
This framing is closely related to the classic SE Bio catchall question "Why do some bad traits evolve, and good ones don't?" The common logic being: "I can imagine a way that an organism could be better, why isn't it already better in that way?" I'm not sure that you are specifically interested in that as opposed to a more general curiosity, otherwise it'd be easier to mark your question as a duplicate and move on.
There are several related reasons I can think of why the level of divergence is what it is, I'll try to hit them here:
1. Evolution is slow
Commenter @user438383 got at this a bit in comments, noting that humans are very young in evolutionary terms and asking why not 99%? There's some logic under there that isn't stated that I'll try to unpack.
Other commenter @Armand posted and then deleted (after a too-pointed critique from me) a version of a thought-experiment: let's build a toy model of evolution and plug in some numbers and see what comes out. For example, we could then say that the expected probability of a site remaining the same across $n$ generations is $(1 - \mu)^n$ in a single lineage assuming no back-mutation, where $\mu$ is the mutation rate. We know that the average site in the (alignable) genome has a mutation rate of around $\mu = 1 \times 10^{-8}$. So if we were to calculate that probability for the average site for $n = 100,000$ generations (~3 million years, way older than anatomically ), we get:
$ Pr(no\_change\_at\_position) = (1-10^{-8})^{100000} = 0.9990005$
So, under this deeply simple-minded model with arbitrarily defined numbers, you actually get very little expected change at the position even for rather large time-scales. There are tons of problems with this model, as alluded to by @jamesqf, namely that we ignore population dynamics. But it should at least illustrate the scales that we are working with here.
2. Many/most mutations are shared, due to coalescence
Another fun subtlety is that, of the mutations that do occur in our toy model in (1), many or most of those mutations are expected to be shared between all humans due to coalescence. Briefly, under reasonable assumptions about breeding dynamics, you expect that all humans share a surprisingly recent common ancestor. So there is no variation, because all humans share the mutations.
This issue is exacerbated by so-called population bottlenecks, which are inferred to have happened fairly recently for humans.
3. Most mutations don't matter.
We have known for some time that most of the mutations that do occur have no effect, and allele frequencies suggest no selection occurs on most genetic variation. So there does not seem to be any particular advantage or benefit for humans from having more mutations.
In the absence of selection maintaining a new allele, it is usually lost from the population due to random chance, i.e. "genetic drift".
4. Mutations that matter are mostly bad.
Of the mutations that do have some effect, selection mostly tends to remove them because they are deleterious. These alleles are removed from the population at high frequencies, leading to an incentive to minimize mutation rate to maximize viable offspring.
In fact, the burden of past slightly deleterious mutations retained in the population is a significant force in evolution (the "mutational load"); it is simpler to just not have these mutations in the first place.
Conclusion: you should expect human genomes to differ very little from each other in the alignable regions.
To sum up:
- There has not been enough time to introduce all that many mutations into the alignable region of the human population genome.
- Of the mutations that occurred, most are shared by all humans.
- Of the mutations that occurred, most have no effect, of which many are lost due to genetic drift.
- Of the mutations that occurred and had some effect, most were deleterious and were purged by selection.
