Yes, AWS is buying IPs for ~$50 so either they're only expecting IPv4 to last for 2-3 years (not) or this charge is basically a penalty for people who are bad at networking.
Even for people good at networking but using managed services, public IPs on instance can make sense. IPv6 support also has its own set of issues.
You mean customers? I can't access IPv6-only websites because my ISP doesn't support it. Oh, and I have the best ISP in the area but none of the ISPs here have IPv6 support.
If you mean routing multiple servers through one that uses IPv4 so you only have to pay for 1 machine then yeah, I guess I'm bad at networking, that does not sound like something I want to maintain.
This is called a NAT gateway and it's AWS networking 101. If you're not willing to learn how to use AWS then you're going to get ripped off.
In that case this may be preferable: https://docs.aws.amazon.com/vpc/latest/userguide/VPC_NAT_Ins...