It is useful for you memorise, there are 2 ways to read of Kanji. 1,On-yomi It is on-yomi when you read "ni" On-yomi derive from Chinese reading. 2,Kun-yomi "Futa-ri" is kun-yomi. Kun-yomi is Japanese reading. We use kun-yomin not only people but things. １人＝Hitori 1つ=Hitotsu An apple=Hitotsu no ringo You can say also "1個=ikko" 2人＝Futari 2つ＝Futatsu Two orange=Futatsu no orange. You can say also "2個=ni-ko" But sorry, I don't know well why we use Kun-yomi only 1 and 2. Maybe it is because the sounds are good. But 12人、22人・・・are read Ju-ni-nin, Niju-ni-nin. And you just memorise how to count.

In your theory, not "NI RI", but "NI NIN", because "人" when you count people pronouce "NIN". "一人"and"二人" are irregular pronunciation. But, in your theory is right. In 1948, "二人" only pronounced "NI-NIN", after 1973 it can pronounce also "FUTARI" both is right. However, some have to pronounce "FUTARI" and some "NININ". "二人で" you have to pronounce "futa-ri-de", today. I don't know why changed. You can pronounce"NININ" with these kanji 二人三脚(ni nin san kyaku)、二人称(ni nin sho)、二人前(ni nin mae) etc.　

In Japanese there are many exceptions in the words they use when counting, depending on what it is you are counting (eg. people, flat objects, tall objects, etc.) If that makes any sense... (◎_◎;) So counting people is a bit tricky as well. people/person = 人 hitori = 1人 = 1 person (hitori de = alone) futari: = 2人 = 2 people sannin = 3人 = 3 people yonin = 4人 = 4 people gonin = 5人 = 5 people ...

1人, 2人 and 4人 have special pronunciations, respectively hitori, futari and yonin. They are exceptions. For other numbers, the counter 人 follows the rule "number + nin" :)

Thank you everyone. All of you were helpfull