Err... math is off.
100 (rate) * 7 (full work day, don't get paid for lunch) * 5 (number of days in a week) * 4.3 (number of weeks in a month) = 15,050
That's 15K. And that's assuming you have a 100% full schedule and spend 0 time on invoicing/marketing/non-billable activities. Realistically, you're probably looking at a 10K rate per month with a 100/hour rate.
The only way you'll see 20K is if you're the middle man hiring the help or you're not billing hourly/daily/whatever. Assuming you're not in the business of managing other engineers, not billing on time increments means fixed price jobs.
Unfortunately, there is only a sliver of work that will fit well into that model. Where the job is very well defined, simple enough to do in a few hours, but complex enough that it can't just be handed off to any random joe. Not too many clients with that kind of work on a consistent basis.
So the OP is right, the only way you'll see that kind of money is once in a blue moon, if you specialize in something niche and can charge 250/hour, or if you're managing other people.