The argument is one of efficiency and load distribution. Base load power plants are capable of greater efficiency than variable ones. This is down to optimisations made around specific output levels and the infrastructure required to support said loads. For example if you know the characteristics of your power output and that of the grid you can build a transformer or switch mode power supply to bridge that specific gap. This outperforms variable input transformers in every case.
There is an argument that low efficiency doesn't matter if the source is renewable, but this fails to take into consideration the embodied energy cost of producing renewable generators, not to mention the increased cost. An inefficient system may not produce enough energy over the course of its lifetime compared to the energy it cost to make.
Finally, most sources of renewables are intermittent and are not necessarily related to the population's power consumption. This makes the storing of energy necessary in order to regulate supply. Storage of energy is a large source of inefficiency and one of the key areas that is being focused on. Base load plant is absolutely necessary to minimise this inefficiency as much as possible.
For a good overview I recommend this site from Penn State Uni: https://www.e-education.psu.edu/eme807/node/667
What do you mean by a distributed power grid? Do you mean power generation happening locally? This is already a thing and is growing in the form of Combined Heat and Power. This doesn't get rid of the need for base load, the overall grid will still need balancing and will still have a base load unless you plan to disconnect local grids from each other in which case welcome to Texas...
Money is not the point here (even though nuclear really doesn't cost much per kWh). I'm talking about the need to build a system that will produce more power over it's lifetime than it costs to make. This is still something that is surprisingly close in many cases so any extra bit of inefficiency risks making the overall system pointless.