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.