Mexican businesses can have dollar accounts at their banks. This way, one can avoid the effect of converting dollars to pesos and loosing value of your cash dollars as the value of the peso moves downward. However, you are correct in that there is a monthly limit to the amount of cash deposits you can make and there is a tax on cash deposits.
The problem of maintaining cash outside of the bank (whether on the books or off the books) is that to get a deduction for any business expense over 2,000 pesos, you must get an electronic invoice that is generated by federally-approved invoice-generating software AND pay that invoice with a bank transfer, check, or bank card. That invoice automatically goes to the Mexican IRS (SAT) for their approval and storage before you get to use it as a business deduction.
The system is designed to make money laundering difficult, but it also has the effect of making it difficult and expensive for small businesses and businesses in tourist areas that deal in dollars. I suspect these tough new laws also drive a certain amount of business dealings "off the grid".
As far as the amount of a business' profit going to the federal government, bear in mind that besides the "cash deposit tax" (and payroll taxes, etc.) the business income tax starts at 30% (unlike 15% in the US) and is collected monthly as a calculation of sales without regard to deductions, which are only taken into account by the federal government at the end of the tax year.
Doing business in Mexico is not for the feint-of-heart.
Yes but just like in the US, the amount of income you declare is what determines your taxes. In the US we have a large cash/undeground economy, estimated somewhere around two trillion dollars. The IRS here does it's best to get as much income declared as possible to maximize tax revenue. But it doesn't stop somebody all the time from not declaring cash income. In the US you can go a loooooooooooooooooooong time not declaring all your cash income, the short term benefit is obviously the cash you have to spend, the long term detriment is you short your business worth if you want to sell it, you short your declared income for purposes of getting credit for instance to get loans for the business or personally say for a home mortgage. However, there are plenty of people who go for the short term benefit of declaring the least amount of cash income as possible and I'm guessing it's no different in Mexico and I suspect it's even more accepted there then here and more prevalent.