The PS2 is one of those consoles that had fairly bizarre hardware architecture compared to say, a PC for example.
Developers took a few years to figure out the hardware and really learn how to take advantage of it. They didn't get much or any pre-release dev time, so they were learning how to use it while gamers were just getting their hands on it. Thus, the better titles came later in the consoles life.
I specify my LAN DNS servers (2 pihole instances, main + a backup for redundancy) in my routers DHCP settings, so they are the DNS servers handed out to all LAN clients; then I have an iptables rule on the router blocking all port 53 traffic from leaving the network unless it came from those LAN DNS servers. This means only the piholes can reach external dns; everything else is required to use the LAN DNS servers or receive no response. Then the piholes have full control over what can and cannot resolve to an IP.
I haven't found a device that doesn't work with this setup. I used to have a couple google homes before I wised up, they worked fine behind this setup.