In Texas and Massachusetts you can actually pick your power provider while paying the natural monopoly for the wires. In time I hope we all can do this.
So assuming the pipe maintenance is done at cost, with no money not being spent on the network. What would your better net positive solution even look like?
But we need to build the nuclear reactors first.
In the mean time, no: people can’t just freeze in the dark.
If you do put in heat pumps, nuclear reactors are still one of the more expensive ways to heat a home, but you need a third as many of them as compared to the no-heat-pumps case, if you insist on heating only with nuclear power.
Nuclear power is really only important if you also want spicy atoms, because it's by far the cheapest source of spicy atoms. Annoyingly, this is now a thing a lot of countries have a solid reason to want.
If only they could sort the underground cabling...
A comparison: the giant Dogger Bank offshore wind farm project (multi-GW) cost somewhere in the $10bn range. On the other hand, Germany calculates with >$100bn for grid buildout within the next decade (https://www.netzentwicklungsplan.de/sites/default/files/2023...).
Also, having customers that rely on your grid but buy very little of your power is simply unappealing for operators, so I would assume that their pricing tries to disincentivise as much as possible (=> "they gonna overcharge you for the grid connection").
Nuclear advocates, like myself, claim drop in replacement nuclear power reactors at existing coal / gas sites would largely obviate this.
Even adding new nuclear power reactors at greenfield sites would constitute a significantly reduced grid build cost, as the power is highly concentrated.
And nuclear is so say that nuclear power reactors employees are routine exposed to less radiation at work than they are at home in their kitchen with granite bench tops.
YIMBY.
At this point, I don't believe in a nuclear renaissance, because it seems to me that nuclear power got left behind too far; catching up in cost metrics is already hard enough, but matching growth rates (in "installed TWh/a" of wind/solar) seems virtually impossible by now. The only remaining holdouts (China, US, France, ...) are basically doing it as a hedge and/or to keep/obtain related engineering capabilities (and at the very least an easy path toward weapon-grade material).
It is clear to me that no one "actually believes" in nuclear power (by stating clearly: we are solve gonna current and future energy problems by mainly relying on freshly built nuclear power), so I can only see its relevance dwindling (I'd argue that China comes closest, but even they are much more in the hedging/securing capabilities category than anything else).