This plan runs into a couple problems.
1. The aforementioned fees for credit card use. Most people are not willing to eat the fees for the miles, as it usually is not worth it.
2. If you charge a lot to a card and are getting cash/checks from friends, the IRS may come after you and want you to pay tax on that "income". I have heard stories of people who could pay their rent with credit cards. They had friends who paid with checks and simply asked the friends to write them the checks so that they could use the credit card to charge the rent for the miles. The IRS sees that you are getting this money from friends and they decide to view it as taxable income and you are left to prove that it is not income. I will pay restaurant bills and collect the cash from friends and such, but I have not sought the opportunity to do it for larger amounts on a regular basis. If you did end up paying income tax on it, those would become some pretty expensive miles.