I'm not aware of Texas passing such a law, but there are some incumbent politicians who might like to if they thought they could get away with it. And recall that the Congress passed a similar law (the Sedition Act) less than a decade after the adoption of the First Amendment.
I think that your interpretation of the Fourteenth Amendment's due process clause is entirely legitimate. An interpretation that just imposes procedural (rather than substantive) requirements on states has a lot to be said for it. For one thing, it seems more democratic to allow states to write their substantive laws in the legislature rather than in the courts. One drawback is that once the Court lets the state legislatures know that they will be reviewing only their "procedural" laws and not their "substantive" laws, there will be times when state legislatures will try to fool them by dressing up and disguising some their more questionable procedural rules as substantive rules.
Note also that a Court which adopted your interpretation would not escape criticism from all sides. Since you would have to overrule Roe v. Wade and allow states to outlaw abortion, you might called be a fascist (at the least a sexist) by some in the pro-choice community. And since you would have to affirm the constitutional validity of any anti-gun laws that a state or local government might pass (because the Second Amendment does not directly limit state laws), you'd be hearing critical speeches from the NRA. And, for the same reason, of course, you would not have been able to join Rehnquist, Scalia, Thomas, O'Connor and Kennedy in utilizing "substantive due process" to declare unconstitutional (First Amendment) the New Jersey law which required the Boy Scouts to accept gay scout leaders. Your critics would then hold you ("and others of your ilk") directly and personally responsible for the breakdown and decline in our country's moral values.
That's the kind of thanks you'd get for your interpetation of the due process clause. And you thought that you were doing them a big favor, huh?
The unfortunate truth is that there is no interpretation that will be successful in avoiding public criticism. No matter how the Court chooses to interpret the due process clause, it will be criticized for "making the law rather than just applying the law like it's supposed to do."
I suppose there will always be some malcontents who will say that of every court action, no matter how reasonable, but realistically, there would be much less justification for it than there is now. If you take an honest look at federal court decisions that rely on that one clause in the Constitution, there is virtually no consistency to them. And combined with the equal-protection clause, they can rule almost literally any way their personal preferences take them - even when there is no offending law to begin with, such as the order "desegregating" Boston's public schools, or that real doosie in St. Louis where the federal judge ordered taxes raised on surrounding communities to pay for supposedly disadvantaged inner-city public schools.
And I don't entirely blame the judges; the culture creates the problem, too. Pick just about any high-court ruling on any subject, and observe the criticism or praise that comes from pundits: Virtually nowhere do you see the decision evaluated on the basis of whether or not the writer thinks it's a valid reading of the law; it is only evaluated on the basis of whether or not the writer thinks the ruling would make good policy, so they're outright encouraging judges to act as priestly lawgivers. This is true even of conservatives. Just recently someone here on FR pinged me to a petition to get the supreme court to overturn Roe vs. Wade, which I refused to sign - not because I agree with the ruling (I very much don't, in case you hadn't guessed), but because the petition didn't mention a single word about the Constitution anywhere. All it talked about was how evil abortion is, which I agree it is, but it's not the job of the judges to make that determination. Their only job is to determine what the law says, and leave legislatures and voters to decide what it should say.
And incidentally, what I would regard as a beneficial result of applying the 14th amendment properly (aside from restoring some integrity to the judicial process) would be that states would once again become the formidable checks on federal power that they were intended to be. It's not that I think it would be a good thing for them to start restricting free speech and gun ownership, but that it definitely would be a good thing if they didn't have some busybody second-guessing their laws and policies all the time. The states have tended to allow themselves to become emasculated in recent decades in the shadow of Washington, and it's really long past time for them to get their guts back. I think that even if it does result in some occasional abuses of power by the states, the overall result will be enhanced liberty for the entire country.