Heck, it's also useful if you can connect to control it even when weather conditions make it too hazardous to travel on-site
Operators have worked shifts that last longer than a day. If a storm is coming in very often the power company will put a second set of operators up in a hotel within walking distance (often just a couple hundred meters) so that they can rotate people in and out as needed. This would also hold for having a second set of operators at the backup site as well, so there would be 4 sets of operators ready to go in these cases.
 You could do that with suitable VPNing over the public internet. That way you benefit from its extensive reach, its cheap price, its resilience, the rapid repair time that ISPs offer. All you need to build is a network connection from each of your grid nodes to the nearest internet.
Not done in the US and not allowed by regulation.
 Or you could do it with dedicated leased lines that aren't part of the internet. You'll pay a heck of a lot more, and loads of grid nodes won't have convenient connection.
This is done but usually only between main and backup control centers.
 Or you could put up your own network. (You're a power-grid so you're used to putting up networks!) But this isn't your core competence, will suffer from longer outages, and will be most expensive
How do you think they are currently getting the data from substations and other devices. It isn't like DNP, Modbus, and ICCP haven't been around for ages and run just fine over the old serial connections that the power companies put in originally. Often they now have a serial to ethernet aggregators and then run just one line back but the power companies do know how to do this and do it well. For added redundancy you can also have microwave link from substations back to the control center which is often the case.
Bear in mind that every subcontractor who prepares a bid using the public internet will produce a *LOWER* bid with *INCREASED* functionality. The only way that a higher-priced bid will ever win is if they someone demonstrate that the downside costs (in terms of expected cost of future hacks) will be significantly larger than the higher upfront bid. And any such attempted demonstration would be instantly met by the answer "why not use just a secure VPN to get best robustness at the cheapest price?"
Yes a contractor could bid that and it may appeal to some of the dumber upper management at a grid operator. The problem is that there are smart people and regulations that would very quickly stamp that dumbness into the dirt. Bring up that doing so is a NERC CIP violation and carries a $1,000,000/day fine and you are talking real money real fast.
So I think that infrastructure like this *can* and *should* be connected to the internet.
Then it is a good thing that you don't work in that industry as that statement proves. You would have had that drilled out of you in your first NERC CIP annual training.