Would be great to get an answer from Steven Harris but I'll take a shot at this.
For the most part, I think you are probably overthinking this. It is not that you are wrong, it is simply that if you are approaching this as an engineering optimization problem there are other variables to consider and coming up with the weights for the resulting trade study will end up veering out of the pure closed form solution into opinion space.
Things to consider
1) If you go with an inverter generator, they tend to be very efficient across a wider range of loads than a more traditional generator. As a result, if you were to attempt to optimally size your system with a traditional generator, you may find that given the shape of the charging curve .e. differences between bulk and absorption charge) , you'd still be better off going with an inverter generator -- of course they are more expensive so you'd have to consider that.
2) The idea of adding a battery bank into a generator mix is trying to address a couple of things a) The traditional generator tends to be burning a lot of gas even at light load so charging the batteries is making use of some of the otherwise wasted capacity; b) You can occasionally run silent (perhaps at night); c) You've got somewhat of an alternate backup power source if the generator fails (albeit not for very long).
3) If you do pick a generator to optimally charge a battery pack v.s. looking at reasonable max household loads, you've got no growth for any heave power draw. The battery bank that many of us add really is not up to the task of being a full house/moderate draw backup.
So, in short, you are not wrong in thinking about this and perhaps you are thinking down a path of two is one and one is none where you have a small cheap dedicated 'recharge' generator in addition to another real backup generator. If that is the case, I also could not fault such an approach as a small generator in that class would not be expensive and I often think about getting a backup generator for my backup generator as well.
If optimizing the efficiency is important to you (and initial acquisition cost is not) then I recommend just going with honda/yamaha, etc style inverter generators that are very efficient across a wide range of loads.