There are a few different reasons why solar and generator do not run at the same time on Franklin systems:
1. Safety - With solar and generator running at the same time, there is a chance of current backfeed into the generator and on sizes of generators on the smaller end of things (in this instance, smaller is less than 60kW or so) that backfeed can cause not only damage to the generator itself but also cause a series of faults that can even result in explosive or fire damage to things around it. If anything, I'm slightly underplaying the safety risk here.
2. Stability - Smaller generators are inherently unstable, and with how AC electricity works, stability is a major factor for all of the components that have to interact with it. Due to how generators work inherently, it means that the rest of the system has to follow it, and if it can't handle whatever non-controlled loads are on the system when they are following it then it creates more issues than it solves to try and have those other sources interact with the generator.
3. Efficiency - While it sounds like having all of the power sources on the system running at the same time would be the most efficient option, this is not actually the case. Most of the time different sources will behave best when operating in their designed capacities. In the instance of Franklin, running the generator while the sun is up is extremely inefficient given the nature of solar power generation. The vast majority of the time the best place to run the generator is going to be at night for short stints to recharge attached batteries and then turn off again. Reducing overall generator run time this way is also the most efficient approach.