You are making a logical step one too far, IMO.
No. Species are arbitrary. Just because you can think of something as one thing does not make it so.
Modern Asian humans have Denisovan genes, modern European humans have Neanderthal genes, African humans have neither. This breaks the Linnean species definition.
Species exist mostly in the human mind. We use the concept as a useful tool to sort out diversity in living things. There is no universal law of nature to dictate species.
https://en.wikipedia.org/wiki/Carl_Linnaeus
Carl von Linne (Linnaeus) created the rules for binomial nomenclature.
At a graduate level, you learn that just because you can place something in a taxonomic cubbyhole for convenience does not always relate to what really happens in Nature.
Why? How about examples:
Examples: Quasipecies concept
Viruses are awful fits taxonomically, so we had to break the "rules" to make classification more useful and not confuse everyone, so we label them as a quasispecies and then we resort to this kind of thing:
https://www.avma.org/sites/default/files/2020-02/AVMA-Detailed-Coronoavirus-Taxonomy-2020-02-03.pdf
Virus do not reproduce like most plants and animals - they hijack cell machinery to churn out lots more virions. And a lot of these new virions are not identical, about 5% of the new virions Covid spewed out have one or more mutations. Which breaks that chart's usefulness long term. The Omicron variant is an example of this.
How bad is this? Well, fairly awful for people who feel they must use things like that chart in the link above.
This is closer to reality (Omicron is the five red dots way out on the right):
https://nextstrain.org/ncov/open/global
Take home point:
But nobody actually uses binomial nomenclature for Covid.
Plants do not play the species name game either. Plants have to have an even number of chromosomes sets to produce healthy viable seeds or spores. That number has to match from the male to female sources.
So, how about a plant species that is not a species by the interbreeding definition?
Switchgrass (we still use Panicum virgatum as a species name). It violates lots of taxonomic rules.
The plant is clump of stems, florists dry it and use it sometimes in making floral display. Pretty.
But one clump can be 8, 10, or 20 completely non-interbreeding "things", since we do not call them separate species. We cannot tell them apart without using a microscope, taking samples at just the right time of year and counting chromosomes. Otherwise the plant stems in your clump are indistinguishable.
They do not interbreed very well. But we cannot tell them apart to know who mates with whom.
Humans have two chromosome sets, think of the sets as "ploids". We write 2n to mean two sets, or diploid.
Can you count in Latin and Greek...? 2n=diploid, 3n=triploid, 4n=tetraploid... and so on.
Switchgrass clumps do not play fair. A stem can be one of several possible ploids. So pollen from one stem may not be able to fertilize an adjacent stem's female flower.
A lot of plants, especially cultivated ones, have extra sets of chromosomes. Because more sets increase the size of the fruiting body or seed: modern wheat=6n, strawberries=8n. Humans played with this fact as you can see. So switchgrass is not the only plant to do this. Some ferns are like 50n and more.
Bottom line - living things are not always a perfect fit for the species definition. Humans, ancient or modern, are living things. Do not overthink the use of a definition from 1761.