Since you can claim self-employment income without documentation, regular audits are necessary to prove actual income. It's also common for people to claim children who don't truly qualify; again, this would only be provable through actual audits.
In contrast, the average middle-class taxpayer tends to have both less built-in incentive to game the system and less flexibility (as most of their income will be documented to the IRS).
To defend the IRS a bit more: this program is in some ways an administrative model. Taxpayers don't need to prove any need to claim the credit. There aren't multiple rounds of paperwork, and, if you aren't audited, the only interfacing you have to do with the bureaucracy is in submitting your tax return, and you'll have money deposited in your bank account in a week. It may be the most effective welfare program, even accounting for audits (many of which are triggered by obvious red flags) in its ratio of benefits to "hoops needed to jump through."