Electric power can be distributed over hundreds of miles with minimal losses.
The line feeding my house originates at the substation as a 12,470/7,200 volt wye circuit. That is a very common distribution scheme in the US, and it’s a big step up from the old delta circuit that my utility previously used. Either way, you don’t want that 7,200 VAC anywhere near your system.
My audio system uses dedicated, derated 20A lines and my utility - which is not a very good one, by the way - has no trouble delivering power on demand. If there is any doubt about your utility’s ability to deliver sufficient power, a "beast of burden test" will settle it. You would need a massive bank of batteries and capacitors to come even close to delivering the power a proper utility offers.
Shunyata Research believes in what is called Dynamic Transient Current Delivery. Another audio forum describes DTCD in more details and I won't repeat the whole concept here. From what I understand of it, power supplies pull current from the crests of the sinewave. So the rectifiers are only open during a small part of the sine wave. When the rectifiers are open, the instantaneous current that flows through to the power supply's storage capacitors can be 10 to 20 times the average current. For example, if an amp draws 10 amps average, the instantaneous current can be 100 or 200 amps. This doesn't blow the breakers because the average current is still below the line's rated current of 20A. For the power supplies, it's best to get the number for the instantaneous current to be as high as possible. Upgrading from a 15A line to a 20A line, using audiophile outlets, using audiophile power cables, are all actions that would increase instantaneous current.
The point I'm trying to make here is that one has to look at what is immediately connected to the audio system's power supplies. This is the power cables, the power conditioner, the wall outlet, the 20A line, etc. The quality of all those things would affect the instantaneous current. In my decade in the hobby, I've found all of these things to be very important. It's not just theory to me since I've proven it to myself over and over. So I'm not really talking about total power or maximum average current. I'm talking about instantaneous current to the power supplies which can be very different in two power delivery systems even when those two systems can provide the same average current.
So how does all of this tie back to batteries and inverters? Here are the positives I see that can help increase instantaneous current for a battery/inverter. The total length of wiring from the battery and through the inverter is very short. I'm using the high current terminals of the Giandel inverter which I believe can provide 41.67A of average current. Generally, the higher the average current, the higher the instantaneous current. It's difficult for me to know for sure if these qualities actually give my audio system more instantaneous current versus my previous 20A line. Shunyata makes a device they call a DTCD Analyzer that can be used to measure but I don't necessarily want to buy one, assuming they would sell one to me. I had to follow my ears on this one.