I see a lot of confusion in the comments about why cell towers would be impacted. Load shedding in the grid occurs across regions of the grid. The power companies don’t choose which specific sites to cut off. If cellular infrastructure is in part of the grid that gets disconnected, it will go down too (after exhausting its backup supply).
The top priority for keeping power on goes to grid segments with life-sustaining equipment. If you live within a grid segment that also powers a hospital you will likely not be subject to load shedding.
The critical detail is that the batteries are configured for standby service, not cycling service, which means that they don't recharge quickly when power comes back on. They're set to a float voltage which maximizes battery service life (years), at the expense of cycle time (hours).
The first time power cuts, you might have 8-10 hours to run on battery. But if it comes back on and then goes off again just a few hours later, the batteries might've only recovered 3 hours of charge. Increasing the recharge rate wouldn't be technically complicated (just adjust the rectifier output), but it would have a logistical cost: These rectifiers aren't designed to be fiddled with so it would take a bit of skill, and someone with that skill would have to visit every site.
Worse, by boosting the rectifier voltage, the batteries would then fail faster, as commensurate with cycling rather than standby service. A site that normally gets 10 years on its battery plant might need new batteries every 3 years, for instance. That's a bad deal.
(And no, the rectifiers simply are not set up to do multi-stage charging. That would add a bunch of coordination and complexity that's just not needed in standby service where they can output a simple float voltage and be done with it. Changing that would be a forklift upgrade, replacing the simple rectifiers with complex chargers.)
It's reasonable that new sites may be installed with lithium batteries someday instead of lead-acid, and that may already be occurring in some places, and that would solve the problem quite simply because lithium just has such higher charge acceptance rates. You can float-charge a lithium and still use it in cycling service because it absorbs charge much more readily even on float. Lead-acids charge incredibly slowly on float, which is fine in a standby application, but it might be the Achilles' heel here.
You missed a critical point that by increasing the charge rate of the battery you've also increased the load on the grid, exacerbating the original problem.
In Pakistan we have had daily blackouts for almost 15 years, though things were better in urban areas recently. Basically, everyone in the middle class has a UPS, with battery to power lights and fans for several hours. Except these are maybe 70-80% efficient. So, yes, the grid has had to deal with, in a very real way, with the increased power demand of millions of households.
> "It [Enedis] said it was able to isolate sections of the network to supply priority customers, such as hospitals, key industrial installations and the military and that it was up to local authorities to add telecoms operators infrastructure to the list of priority customers."
This is also a good argument for mesh-networks between cell phones independent of cell towers, although those don't scale for large numbers connected phones and large numbers of users. Texting could be supported via such mesh-nets easily I imagine, but not video.
Indeed, a large part of cell towers are hosted on the rooftop of residential buildings and mostly connected to the same electrical network.
In France, most homes have a smartmeter (called "Linky") and these could be used to have very precise load shedding (they communicate with PLC) but I believe this feature is not available or developed (yet?).
The top priority for keeping power on goes to grid segments with life-sustaining equipment. If you live within a grid segment that also powers a hospital you will likely not be subject to load shedding.