The Commerce Dept first issued calls with just 3 letters, not having any idea how popular broadcasting was to become. They ran out of 3 letter calls by March of '23; WEV was the only Houston station to ever have a 3 letter call (while licensed to Houston). The original dividing line between the Ws and the Ks was the Texas-New Mexico border. By January 23, they had figured out there were going to be a lot more requests for permits in the Eastern US than Western, due to population, and moved the line to the Mississippi. The first station issued a K-call that would previously have been issued a W-call was in Houston, KFCV, in January, 23. It was licensed to the Mahaffey Electric Company and lasted 3 years, at least on paper. It only broadcast to demonstrate radio to potential customers within the store.
There were no computer generated random lists so the government relied on serial lists. The pattern established for the first W-calls was W_A_, with the blanks filled in alphabetically. All the stations in Houston and Texas that got W-calls followed that pattern, WBAP, WFAA, WTAW, WOAI, and WJAD, Waco among them.
TJRG is correct that none of the stations licensed in Houston in 1922 survived; our oldest local station is now KHCB, League City, 1400, originally licensed as KFLX, Galveston, in November, 1923. It was later KLUF and KILE and is the oldest station anywhere on the Texas Gulf Coast.
WJAD is an interesting exception - it flipped to WACO in 1930, well after the move of the line to the Mississippi, after persuading a merchant ship to give up the calls and apparently persuading the FRC to allow a W-call west of the Mississippi. There are other notable examples of K-calls east of the Mississippi besides KDKA, which by the way, was not the first radio station; another one is KYW, Philadelphia, another Westinghouse station, that started out in Chicago and spent time in Cleveland before winding up in Philly, each time being allowed to keep it's original calls.
Besides WACO, the only W-calls issued in Texas that I know of after 1922 were those issued to FM or TV counterparts of AM stations with W-calls, again, allowed by FCC rules.