Note that these are state laws. The Alex Jones judgment still has to wind its way through appeals, but like you say there's a good chance the cap will be protected by the Texas Constitution.
Ohio (Oberlin) has a similar cap, but not necessarily the same protection for it. Missouri for example also had a cap, but it was held to violate the Missouri Constitution in 2014.
The Missouri case[1] came up last month post-Alex Jones, and its "separation of powers" argument is interesting. There's a professor at Georgetown who thinks a similar argument could succeed in Texas[2], but Texas at least tried to amend their Constitution to allow the cap[3].