Inverters : 12V vs 24V?
As the inverter power level goes up, 12V inverters become totally impractical due to the required wire diameter. For example, if you have a 4kW inverter, it would be really ridiculous to design it for 12V. 4kW/12V = 433A. Even at 1kW, you are pushing limits with a 12V inverter.

There are a lot of really junky inverters out there. If you see a high power inverter that takes 12V, there is a good chance that it is a piece of junk, and that the ratings are wildly optimistic.

For off grid home use, I would recommend you work with the highest battery voltage that is practical (which is  generally 48V). This will allow you to use more reasonable wire diameters without power loss. Power loss in wire is a function of I squared, so it makes a big difference. And copper is expensive. And fat cables are difficult to work with. Etc.

If you can't or don't want to work with 48V, then 24V is the next best thing.