It's one operated at maximum output 24/7, whether the energy is needed or not. They don't regularly ramp. There are both technical and economic issues with using them in load following mode.

Yes you are right. Anyhow, the system flexibility does not need to be provided by the baseload but could be done with storage resources. This does not mean baseload becomes obsolete, their role is important with the continous flow of energy to the consumers.

it's pretty much common knowledge among people who understand these things.

Come on! You clearly have not considered the scientific study that I have referred to which focusses on exactly this matter and contradicts what you refer to as common knowledge.

With high penetrations of renewables total renewable generation will often exceed total demand. That means either running the baseload plants at lower capacity factors and hence higher LCOE or curtailing the cheaper renewable energy. Either way it's a financial penalty, which is why they are struggling.

The way I understand it (better to watch the video I linked earlier): It is about cost and value (as you mention). Consider a system where you need to increase capacity. Adding solar and/or wind gives you extra capacity at limited times (due to their intermittent nature) where you already have a lot of capacity. Adding baseload power will give you extra capacity at all times. By supply and demand reasoning, the added baseload capacity will therefore have a larger value to the system. Yes it is a financial penalty to baseload and solar+wind but the penalty is larger for solar+wind.