I don’t think you are understanding how this works.
If a bass amp is rated to draw 3 amps at 1/8 power (fairly large amp), the sizing for battery life is based on this long term average by multiplying the current by the line voltage giving 360 watts, then multiplying by the inverter efficiency of say 80% or 420 watts.
Now you look at the battery capacity. Multiply the AH by the voltage and you get watt-hours. Say your battery is 12V and 100 AH, that would be 1200 Watt-hours but a standard lead acid car battery has discharge limits of about 50% which gives you 600 watt-hours of capacity.
Now, divide the capacity by the load and you end up with the hours of run time, or in this case 600WH/420W or about an hour and a half.
For inverter SIZING, it must be capable of supporting the dynamic load which includes the short term peak currents. A good rule of thumb for class D bass amps is roughly 50% of the audio power, converted back to AC line current. So if the amp was rated at 800 watts into the load being driven, that would be 400 watts, which is the minimum the inverter would need to be rated for independent of the battery side of things.
I have worked with audio, AV, musical instrument/PA amplification and 12V audio for over 45 years- I also repair boats, including the electrical systems- I'm pretty aware of real world applications for this.
I have a 400W inverter- it's not very big and it wouldn't like to power a bass amp for long. I use it for charging batteries for my power tools and sometimes, for my laptop. Its rating might be called 'optimistic', but I haven't tested it- I don't expect it to do hard work for that price.
We actually agree on some of this- the load side needs to be known before the battery side.
Battery reserve capacity is rated in Amp-Hours- it's right there on the label. You can't use a battery until it's dead and reserve capacity reflects the battery type's ability to maintain its voltage under load.
The link is for a company that works with marine electrical systems and the company owner is an Electrical Engineer-
Battery Bank Capacity Calculation | Pacific Yacht Systems
