Why not pipe it over the internet? A few redundant ISPs at the endpoints should be as reliable as a private run of fiber or T1 lines or whatever bespoke solution they think they need?
The fiber is already there, and it gives you guaranteed capacity, even during a major power outage. And it guarantees no one is changing out a switch or a router at a bad time, etc.
It’s just a lot less to control and to go wrong.
There's no argument that a private line is ideal for critical infrastructure, but if they must make do, there are ways to make it work.
Anyone not behind one of the major CDNs can be targeted and taken down. And bandwidth-exhausting a few routers in front of the target is certainly possible, it's just not profitable for cybercriminals - but for a nation-state? No problem at all to muster a few terabit/s of capacity for them.