I haven't read the book so I can't comment on it, but if its premise is anything like the cartoon @BondiandBabe shared, then the logic is deeply flawed.
Yes nurses, doctors, law enforcement etc, are vital jobs, but that doesn't mean other jobs are bullshit. It's important that an economy is healthy enough to adequately fund these bullshit jobs, and that's where the other jobs come in. And it's simplistic to think that we could go back to trading skills instead of money... It's logistically impossible given medical and technological advances, and the training and capital necessary to maintain these standards... and given the population sizes.
And why has the comic writer drawn arbitrary lines of what's a vital and what's a bullshit job. A tax advisor is a bullshit job but an artist isn't?
Anyway I've realised I can't be bothered to deconstruct the comic since I couldn't really get past her saying that women only really entered the workforce 50 years ago. A basic history lesson would shows that's completely inaccurate. Women only started doing professional jobs relatively recently, but cooks, nannies, governesses, maids, farmers, mill workers, seamstresses... throughout history women have worked in numbers except for the upper classes.