Why do you need to smooth pricing? By allowing prices to rise and fall throughout the day in response to supply and demand, you don't need to add supply between the time the sun goes down and the time people go to bed at night.
In other words, you can treat it as an economics problem and save your customers a lot of money on power plants and fuel. This is why the world is switching from flat rate pricing to time-of-use pricing.
The goal isn't to smooth pricing...it's to smooth the peaks and valleys of demand.
The grid has to be built for peak, not average...in other words, if 5% of the time, the total load of a utility's customer base is 4.5 gigawatts, then they have to be able to provide 4.5 gigawatts, even though 95% of the time the demand is half that, at most.
Ideally, power demand would be flat and constant...the same amount, all the time. Steam plants experience metal fatigue when they throttle up and down, and this is already a major problem with most utilities now. It's also way harder to regulate an efficient burn at multiple rates...which in turn, means it's harder to regulate emissions, which leads to limits on capacity if they exceed emissions of certain sorts (and, just to make it fun, those standards have just been tightened...a LOT). Those are both a big deal: too much leaking in the heat exchange coils in the boiler, and the whole plant has to come offline. Even getting close to the limit on emissions for a period, and the plant comes offline to avoid overshooting it...the plant goes into reserve mode, needed only for emergencies. And this, in turn, increases the impact of the peaks/valleys situation on the rest of the utility. And what I just described assumes 100% controllable, fuel-based generation (nuclear, petroleum, coal, gas). Now, these peaks are predictable (and predicted...there's a whole industry around the metrics and predictive load management involved), but it still poses a challenge. The steeper the walls of the peak, the faster and harder you have to spin up the generators, and the greater the stress, as well.
Renewable energy is great, except that it throws another wrench into the works. Let's say you're getting a lot of your power from solar...but then clouds move in. Effectively, for your non-renewable generation, you've just introduced a peak because it has to throttle up to take up the slack. So you end up with lots of peaks of various sizes, instead of the one or two big peaks per day. And even worse, these peaks aren't predictable.
If, however, your solar generation capacity includes a way to continue generating power after the clouds roll in, you've done two things. One, if the cloud layer is short-lived, you're able to simply disregard it and life goes on. Two, if it isn't, then you've bought more time to spin up capacity more slowly...which means less stress on the boilers, and also more options to choose from. Maybe you fire up a CT peaker, which has less trouble with variable load but takes 20-30 minutes to come online, for example. But ultimately, what you've done is taken one of the biggest problems with renewable generation and dramatically reduced it.