Can you apply for readmission from within the U.S. after an illegal entry? C'mon.

You're talking about 8 CFR 212.2(e)? That provision is obsolete following the passage of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996. I don't know why it hasn't been updated. See sections 241(a)(5) and 212(a)(9)(C)(i) of the INA.