I doubt regarding the six realms as 'physical reincarnation' can explain the statistics of people because the Pañcagatipeyyālavagga of the Samyutta Nikaya says only a few from each realm will attain the status of "human".
If we read all of the very short suttas in the Paṭhamaāmakadhaññapeyyālavagga until the end of the Pañcagatipeyyālavagga, we may possibly gain the impression the word "human" does not refer to something biological & reincarnated but instead refers to something mental & behavioral. The very first sutta here, titled "Not Human", says:
In the same way, the sentient beings reborn as [having comparative status of] humans are few, while those not reborn as humans are many. Why is that? It’s because they haven’t seen the four noble truths. What four? The noble truths of suffering, its origin, its cessation, and the path.
The strong impression above is the word "human" refers to "having seen (diṭṭha) the Four Noble Truths".
Again, suttas, such as SN 56.47, give the strong impression the word "human" refers to a mode of conduct rather than to a biological state from reincarnation. SN 56.47 says:
Sooner, I say, would that blind turtle, coming to the surface once
every hundred years, insert its neck into that yoke with a single hole
than the fool who has gone once to the nether world would regain the
human state. For what reason? Because here, bhikkhus, there is no
conduct guided by the Dhamma, no righteous conduct, no wholesome
activity, no meritorious activity. Here there prevails mutual
devouring, the devouring of the weak. For what reason? Because,
bhikkhus, they have not seen the Four Noble Truths. What four? The
noble truth of suffering … the noble truth of the way leading to the
cessation of suffering.
There are many suttas similar to the above, such as AN 6.39:
it’s because of deeds born of greed, hate, and delusion that hell, the
animal realm, the ghost realm, or any other bad places are found....
it’s because of deeds born of contentment, love, and understanding
that gods, humans, or those in any other good places are found.
Iti 93 gives the impression the lower realms comprise of "mortals". The Pali here is "macca", which means "a man"; and "pajā", which "this generation of people" or "mankind".
The fire of greed burns a mortal (macca), lustful, infatuated by sensual
pleasures; while, fallen in the fire of hate, a person kills living
creatures; and, bewildered by the fire of delusion, they miss the teaching of the noble ones. Not recognizing these three fires, people (pajā) are caught up in identity.
They fill the ranks of hell, of birth as an animal, or of demons and
ghosts, not freed from Māra’s bonds.
More relevant suttas can be read at this link: The five realms in the here-&-now.
While most Buddhists and many scriptures describe the realms as "physical", there are also suttas that describe the realms as "psychological". When the realms are regarded as psychological, illogical questions can be answered more logically & less speculatively.