These days with batteries, a lot of that demand can be served very rapidly. Batteries act as buffers and increasingly replace traditional back up generation (stand by coal/gas plants). A lot of these load spikes are short lived. There are all sorts of weird spikes related to people turning on their tea kettles in the morning or turning on their stoves around 6 pm, etc.
Battery production is currently shifting from hundreds of gwh per year to twh per year worth of production. They last quite long too. If you cycle 1 twh of battery every day, it would run out in about a decade (assuming 3000 cycles or so). And if you do that, that amounts to absorbing and serving about 365 twh.
The worlds entire electricity production is measured in peta watt hour (pwh). About 25 phw. or 25000 twh. So, with battery production scaling int he tens of twh per year, there may soon be enough battery to absorb and produce that kind of volume. Doesn't mean it will be used exclusively for that. But it drives the point home that we are talking some very non trivial levels of standby power. That's car batteries, home batteries, grid batteries, etc. connected to the grid. Mostly neither charging or discharging most of the time.
Tesla and a few others are starting to experiment with virtual energy providers. That might go from a few GW to having in the order of TW of power available on demand very shortly. There are about half a million tesla home batteries out there apparently. Even a few thousand of those already add up to quite a bit of collective power. Imagine that scaling to millions of connected batteries. They'd be the largest power supplier, by far, in most markets.
That won't run the grid for hours/days obviously. But it does eliminate a lot stand by capacity that is expensive and poorly utilized.
That's also the future for energy intensive industries. They'll want to generate most of their power locally (because that's cheaper) and use batteries to buffer it and fall back to the grid only when that runs out and export to the grid whenever there's a surplus locally. So, that reduces load on the grid and evens out a lot of the load spikes. And a lot of the time they'll be feeding energy into the grid. Anything energy intensive is going to compete on cost. And that means investing in local production and batteries.