No-one said slow. I was thinking FTTP. However a public sector initiative would come with limits. It has to come with limits because people demand low taxes. Let's say the public sector does the math and says 500Mbit is what they can guarantee for equitable distribution to all addresses. That should be plenty for most people. But there will always be one person who demands their god given right to 10 gigabit. In which case you direct them to the private sector and tell them to pay for it on their own.

Wouldn't the private ISP offering 10 gigabits have to lay their own pipes anyway, to support that speed?

Not necessarily. If you lay down FTTP for 500Mbit it'll work at 10 gig no problem. You need to change the equipment at either end. In fact it'll work well beyond that speed if someone wants to pay for the equipment. But if the private sector wants to lay down their own cable in parallel to the public sector then who is stopping them?

Streaming video is not a necessity.