You are confusing operating/marginal efficiency with lifetime efficiency. Think about a power plant as a series of payments. You have one big up front payment to build the thing and a series of smaller payments to buy fuel and run it.
For solar, those smaller payments are zero. There is still the fixed upfront payment and that is why you would prefer 40% efficient panels to 20% efficient panels everything else being equal.
The marginal cost of rooftop solar is zero. Nothing is wasted. Really! No fuel is bought, the roof underneath is cooler and lasts longer, there are systemic benefits, etc. There is virtually no maintenance. No land is used (Solar land use is complicated but most places you can put solar wouldn’t support a nuclear plant). Light which would have bounced back into space or turned into infrared is instead made into usable, high grade energy. Land/build area that would otherwise do nothing is made useful. It is literally close to economic and physical magic. It is true that panels break, inverters die, upgrading is compelling, etc. However, most components are silicon, glass, copper, and aluminum. These are some of the most recyclable materials on earth. There are plenty of analyses of lifecycle energy and material costs and it is generally pretty favorable (1-2 year operating recovery time). The panels are warrantied in many cases for 25 years so idk where your 20 year then scrap lifespan comes from. Inverters tend to be the weaker link.
Finally batteries have marginal round trip efficiency because what you put in doesn’t come back out 1-1 so I am not sure I follow your point.
No, it isn't. There's literally materials consumed to build the solar panels, and a 0.4-0.8 deaths per TWh generated. To your own point a 1-2 year recovery period on panels that last 20 is 5-10% loss in energy off the mark. We don't really have a recycling plan, but we better get one, because solar generates a ton of waste materials. To power the entire United States, we'd need 20,000 square miles of solar panel - the entire landmass of West Virginia. Replaced every 20 years, we'd need almost 100,000 square miles of solar panel in my lifetime. That's the entire surface area of Colorado.
But that's ok because I'm not arguing against rooftop solar lol. I never was. That doesn't change the fact they're not particularly efficient, and there's a lot of room to improve. I was arguing in favor of nuclear, which, with seawater extraction, can be completely renewable.
There isn’t a lot of demand for panel recycling because most panels have been installed in the last 10-15 years are not end of life. When there is demand there will be recyclers, you don’t need to centrally plan it.
There actually is NOT a lot of room to improve with monocrystalline silicon and other single band panels. The theoretical max efficiency on them is 40% so they are currently more than 50% of their max, room but not a lot. The technical efficiency (how much of the energy hitting the panel is turned in to electricity) is subsumed by the economics. For ROOFTOP, small systems can offset residential load 100%. I am not sure what is inefficient about that on any definition.
Total efficiency here is the sum of all inputs over outputs. For solar panels that's land use, that's glass, silicon, plastic, PCBs, etc - in addition to the sun.
Otherwise, in your model, a panel that's 100% efficient is inherently the same as one 15% efficient.
In your model, a battery is infinitely efficient - after all it has no inputs, only outputs! Once you get to that point your model needs to be adjusted.