The difference is that you can give an IP to a device semi-permanently and you can route to it directly if needed. This allows you to configure a firewall in your device specifically, rather than having to orchestrate with the router. For instance, you can give your laptop an IP and your partner's laptop another IP and you can just route everything to those two specific devices, which you know is handled properly by two responsible people. I agree with the point that you probably want to be more restrictive in the router level when you connect your fridge, printer, etc.

Moreover, the router is a lot simpler as it doesn't need to keep track of connections, which works well with TCP, but not necessarily with UDP. So, you can actually use other protocols other than TCP easily too. The only downside of IPv6 is that it is not backwards compatible, but being able to identify devices uniquely has no down sides.