How are you going to host a game server on a home computer if you share your IPv4 address with other subscribers to the same ISP in the same neighborhood,[1] and the combined modem and router that your home ISP requires all subscribers to use lacks an option for port forwarding? Both of these are true, for example, of T-Mobile US Home Internet.
[1] Many home ISPs apply carrier-grade network address translation (CGNAT) to conserve IPv4 addresses since the worldwide exhaustion.
You don't. Because home internet connections, even the multi-gigabit ones, are terrible for things that need constant ping.
It's why people have been hosting services where they can get a dedicated IP, or likely one shared with similar services. Those hosting servers tend to have guarnateed connectivity.
Because direct IP connections sucked, and it's why booter services aren't so common nowadays. Because that's what happened in the past - if you got angry, you started pingflooding the host IP and making everyone's game terrible.
These days, you still have booter services, but they're services you pay for, and they're not used as much because the hosting server often hides the IP of everyone else.
I don't disagree with local servers, but maybe let's leave them on the local LAN plan. If you want to expose it to the Internet, then you can, and if you do, better have the expertise to know how to host it yourself.
And no, IPv6 won't fix this - because IPv6 only guarantees everyone gets a globally unique IP address. It doesn't guarantee that end-to-end connectivity will work. Thanks to firewalls and such which are a practical necessity these days.
The popularity of online multiplayer competitive play is driven in part by centrally hosted servers where there are people who do protect them against attacks meant to spoil the fun of everyone involved. Only a huge data center really has that ability. But if you want to host a small scale server on your own for you and a few friends, you should have the option as well