When it comes to residential/consumer use base load is irrelevant - but when it comes to business (especially industrial) use base load is a strict necessity. The proportional requirements of base load are fading but it is still something that needs to be considered carefully.

Do fossil fuel companies overstate the importance and scale of base load to justify additional fuel subsidies? Indubitably - but don't let their bullshit hide the truth within it that actually is a critical requirement for our power grid.

No, you need to match the demand curve at all times.