But solar would increase the need for peaker plants if it starts replacing baseload power needs. We are a long ways off from that, but it will limit the usage of solar until solar drops below the marginal cost for natural gas usage.

I'd say lets cross that bridge when we get there. Solar is a very long way from replacing baseload power.

And once baseload power starts getting "replaced", we enter the realm of coal plants and nuclear plants reconditioning themselves so that they can be scaled up and down a bit better.

I know both coal and nuclear power require many minutes to change their energy production, but if a smaller-scale energy storage (~30 minutes) can be created to hold out during the scaling up / down period, the problem could be solved.

As opposed to say, load-shifting pure solar energy (which requires a storage capacity measured in hours, not minutes). High power / low time can be solved with standard Lead Acid batteries or maybe Flywheels (cheaper technology than Lithium Ion, which would be better for hours of storage)