There is nothing particularly unusual about any of this. Although federal law guarantees effective legal representation for criminal defendants who cannot afford it, Texas sets no requirements for how quickly they get help. It sets standards for lawyers' qualifications and experience only in death-penalty cases, which are a tiny fraction of the courts' business. Some pay so little that they have trouble attracting competent lawyers, a recent State Bar committee report found. Most counties don't have public defenders, which are common elsewhere in the country.
Judges appoint and compensate attorneys under any number of systems, or sometimes no system at all.
Some judges won't assign attorneys to defendants who can make bail, even if doing it would exhaust their resources so some people sit in cells to qualify for a constitutional right. While these have an immediate effect on the defendant, they also have an inexorable effect on the community in additional welfare and other costs. Last year, the Legislature unanimously passed a bill requiring that indigent defendants who requested an attorney receive one within 20 days. Those who were still in jail after that time without an attorney would be released. Judges had lobbied him hard.