I for one found the commerce clause approach disingenuous and specious.
We might debate the appropriateness of the 13th. However, the 13th clearly provided Congress with the power appropriate legislation to eradicate the "badges and incidents" of slavery. As such, legislation can reach not only to states but also to individuals. We might agree that the power was misappropriated, but the amendment clearly granted to Congress the power under the amendment. I might add that southern states were coerced into ratifying the amendment as a condition of reconstruction.
The 14th and 15th amendments could not be used to reach the action of individuals because those amendments only restrict state action. As such they could not prohibit discriminatory action by restraurant owner or hotel managers in the Jim Crow south. So, the only amendment that could address it was the 13th.
There are several glitches in such an application. First, slavery was abolished in those parts of the South controlled by the Confederacy by the Emancipation Proclamation. As Sherman marched through Georgia, for example, slaves were freed. That proclamation did not free slaves in the four slaveholding states that could not join the Confederacy, nor in West Virginia, nor those portions of Southern states, like northern Virginia, east Tennessee, and south Louisiana, under Northern occupation as of January 1, 1863. By January 31, 1865, when the amendment was sent to the states, the areas still under Confederate control were greatly reduced. By August of that year, Union control was effectively established throughout all the South. By August 1865, Lincoln's proclamation had freed over 95% of American slaves. Slave labor was not a major economic element in the Border states by 1865, nor in the portions of Confederate territory occupied by the Union as of January 1, 1863. What the amendment did was to codify into America's fundamental law the concept that slavery was forever illegal.
That the Border states like Maryland and Missouri and the most conservative Northern states like Ohio, New Jersey, and Indiana ratified this amendment would indicate that the state legislatures believed that the amendment would merely formally abolish what was, by August 1865, a moribund institution.
If segregation was a "badge or incident of slavery" in the South, then what about its existence in Northern states? Keep in mind that the 1954 Supreme Court ruling of Brown vs. Topeka Board of Education was based not on a Southern, but a Kansas school district. Many Northern states had Jim Crow laws; if they did not, they certainly did not prohibit discrimination in the private sector. Also, both law and social custom discriminated against American Indians and Orientals, races that were never subject to mass chattel slavery in America, in many Northern and Western states. Hispanics, Irish, Germans, Italians, Mormons, and Jews, though never enslaved in this country(except for Irish and British indentured servants in colonial times), nor discriminated against by law, were subject to widespread economic and social discrimination.
Additionally, the 13th Amendment has had little penumbrance. It does not forbid a military draft, nor other compulsory duties of citizens that had existed, in the interpretation of the Supreme Court in 1918, from time immemorial. Its extension to the area of private sector discrimination would not appear warranted.