The bigger problem with solar and wind isn't baseline but rather the fact that they are variable in nature. That makes it harder to have a baseline power plant.
The reason natural gas is taking off is that it can quickly respond to differences in production vs demand (it's a peaker plant, as in it handles peaks in demand). Solar and wind make those peaks more pronounced while lowering what baseline can do.
This is why coal plants are dying, they are slow to respond to demand and renewables decrease the baseline that can run at (well, that and fuel costs keep rising due to inflation).
Storage solves both problems. Baseline can be higher, storage will consume it, and peaks are less a problem, storage can handle those.
Alternatively, load based demand would make sense (at least to solve the baseline problem). We could, for example, eat excess energy doing CO2 extraction (though, that only makes sense if baseline doesn't produce more co2 than what we are consuming).
This has less to do with electricity demand than with politics.
True, kinda, but that has more to do with there being no good reason to build a natgas plant that can't be throttled in response to demand. You can use anything for base load if you want but economically it makes more sense to use the cheapest stuff possible for base and more expensive stuff for daily fluctuations and peak. But coal is getting more expensive and gas is cheap so we see more and more base load taken up by gas. Instead of idling in off hours more and more gas plants are running at low capacity to provide a little bit of base power.
The whole base load/peak way of discussing things is slowly going out the window as more and more power comes from renewable since even base load is going to fluctuate around the grid based on the availability of sun/wind and something (currently gas, maybe storage in the future) has to absorb that load.
I really should have framed things in terms of stability rather than base load. With wind/solar you can't be sure you'll have wind/sun when everyone wants power some arbitrary date in the future which is where storage/gas come in. You have a base load but solar/wind can't be guaranteed to provide base power so gas/storage spins up. From a gas plant or battery point of view a dip in solar/wind capacity is no different than a demand peak on an otherwise coal grid.
The good reason not to build an OCGT if you're going to use it for baseload generation is that it's quite a bit less efficient than a CCGT. And the good reason not to build a CCGT for peaking use is that you probably won't recover the additional capital cost (because efficiency for a CCGT won't exceed an OCGT for several hours after startup).
But they can't provide stable baseline power without storage. Storage is not yet cheap enough to be cost competitive with fossil fuel solutions hence why we are still running old coal plants and building new natural gas plants. This is why people are still talking about nuclear. It can provide baseline power but without crapping carbon into the atmosphere. Yes we will have less use for power that cannot be throttled in the future as more of the grid is wind/solar but newer reactor designs can be throttled.
Edit: Yes I know that natural gas is traditionally for peak load but that is changing. See my reply to bryanlarsen's comment.