no they're not. Not when you're dealing with potentially large loads. an extension cord rated for 13 amps with 16 gauge wiring, with a 110v dryer running on it, will cause a fire, sooner or later. A proper 10-gauge, 20 amp-rated extension cord will not.
that this system won't exceed ratings is a fair point, but extension cords are not just extension cords.
Obviously the extension cord you use needs to be rated for the power it carries. Anyone buying extension cords can see there are different sizes. They are well-labeled, and it is easy to look up the gauge needed for its length and what is to be plugged into it. A correctly-rated extension cord is no more hazardous than the same-rated Romex, and often cheaper.
All the appliances mentioned are rated to be used with appropriate extension cords, and cords are sold at retail for such use.
"obviously" is doing a lot of work there. What's obvious to you isn't obvious to the next guy, who's just going to look for the cheapest cord there is.
They're not well marked at Home Depot, you have to bother to look for the right gauge, the cables aren't even necessarily in the right place, and if you don't know jack about being an electrician, it's easy to buy a cheap 2-prong 18-gauge indoor-rated cable for use outside in a wildly inappropriate fashion. No one at Home Depot is going to stop you and ask what you're about to do with the cable.
yes, For people with half of a clue, it's possible to buy the right cable and be safe, but we have to plan for the lowest common denominator, and tell people that extension cords are just extension cords when they come in all sorts of flavors, some of which are happy to burn your house down, is irresponsible.
The store brand, which is general most prominent, gauge is color coded: 6AWG - Gray / 12AWG - Yellow / 14AWG - Pink / 16AWG - Orange. There's one exception to this where 14 AWG cable is using orange labeling normally used on 16AWG wire but that's the opposite of a safety issue.
And they have generally have the rated amperage for the length of the cable.
This all falls under "it is possible to kill yourself by stupidity", with nothing specific to powering appliances from a battery/inverter. People who take the initiative to set up such a system self-select for attention to detail. It is a lot easier to use the wrong cord with no battery system than with.
that this system won't exceed ratings is a fair point, but extension cords are not just extension cords.