Why is classful addressing considered waste?

I am trying to understand the addressing strategies. But there is something which I can't grasp. Maybe I am missing a very basic point, if so, I am sorry beforehand.

From my researches, let's say, if a company wants 100,000 IP addresses for their network, Class C won't cut it since Class C can allocate 256 addresses. Same for Class B since it can allocate 65,536 addresses. So they were asking for Class A which can allocate 16,777,216 addresses but that would be a huge waste of IP addresses.

Now coming to my question. Don't all computers in a company reside behind a public IP address configured by a router? Let's say I have one router for an office in Istanbul which has 185.245.32.78 as the public IP address. All the computers in that office would have 192.168.xxx.xxx as private IP addresses. The same for other offices. I could use 20 different public IP addresses for other offices spreading around the world and have same private IP addresses behind a routers.

Doesn't this mean I could have many offices with networks with only Class C allocation?

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