It both is and isn't a problem, depending on your time scale, and opinions about how we should bridge the variations in supply and demand.
Today, on the short timescale (subsecond) this need is called frequency regulation, and we mostly do that with so-called "peaker plants", essentially natural gas turbines that run constantly and feed power onto the grid at subsecond notice.
This is a very expensive source of supply (easily 5x the median wholesale rates) because the natural gas is mostly wasted (not to mention the very high CO2 emissions: ~600g/kWh produced [1]).
Therefore, there are a lot of companies working toward solutions to this, that don't involve burning fuel, either by building stationary storage, or by aggregating negative demand, thereby participating in a very expensive electricity market with a low-marginal cost solution. In short, this is where the money is today.
The next level for storage is not yet a problem, but will be: storing excess renewable energy supply between different parts of the day or week. The value of this service to the climate is massive, but the economic value of this is not enough to justify the cost of Lithium batteries. To support this use case, we need batteries or other storage media that are 10-100x less expensive than Lithium batteries.
There are many candidate storage technologies for this use case, from pumped hydro to metal-air batteries, to compressed air energy storage, but no clear winners yet.
1. Estimated based on a rough average of .65tons/MWh for CA peaker plants from: https://www.psehealthyenergy.org/wp-content/uploads/2020/05/...
Yes it is. It's one part of the solution to fluctuations in electricity production (renewables: wind, solar) and consumption (day / night, warm / cold).
In a grid, at all time, the production has to match the consumption perfectly. You can make the frequency vary a bit to make up for fluctuations, but only so much before damaging things. Storage helps with a production higher than consumption and then with a higher consumption later.
Good storage makes grids more flexible and ideally lower the need for electricity production, and costs.
I agree with the rest of your comment though.