Seriously, Texas is probably one of the few states where the coaching staff (including assistants) must be full-time school employees; the reason as I understand it that teachers (which are professional employees on salary as opposed to an hourly wage) are coaches is that you cannot offer a straight stipend to an hourly employee (such as a janitor), so the district hiring that person would have to be sure that the total of his/her normal duties AND coaching duties are less than 40 hours per week, or that person would have to be paid at time-and-a-half for hours over that number.
Many other states allow part-time and volunteer coaches in public schools, as do private schools in Texas. Honestly, most of us could not afford to make the expense in hiring all our coaches as full-time teachers or we may be in the position of being sure our third-grade teacher can also coach golf and two other sports.
Unless the legislature/TEA changes that regulation, it will insure that few, if any, private schools are serious about joining the UIL. Which may be best for all of us.