@Bill Gulley has hit the nail on the head.
I am a plaintiff's lawyer here in Texas and I can tell you the issue of asset protection is really, really overblown, at least for the vast majority of SFR investors. The vast majority of personal injury cases (e.g. slip and fall, dog bites, etc.), which is where most claims of liability come from, will never even be close to the standard $1M in liability coverage.
Moreover, here in Texas, most lawyers are smart enough to almost always make a demand within policy limits once enough facts are developed. (This is true even with wrongful death cases, unless there are extraordinary circumstances.) The result is that if the insurance company turns down the offer, and the case goes to trial with a verdict in favor of the plaintiff that exceeds policy coverage, it is the insurance company, not the owner, who is on the hook for any excess judgment.
Another point to consider is that property that is highly mortgaged is worthless to a plaintiff's lawyer. The mortgage lien trumps an unsecured, judgment creditor's lien.
I also reject the suggestion that an insurance company might not defend an insured based on some nit picky exclusion. The duty to defend in Texas (and most jurisdictions) is much, much broader than the duty to indemnify, and an insurance company get in big trouble for violating its duty to defend. I have rarely seen a case where an insurance company has refused to defend if there was any possible basis for coverage.
As a lawyer here in Texas, I can also tell you the bogey man of punitive damages is ridiculously overblown. They are exceptionally difficult to obtain (there basically has to be overwhelming evidence of an almost evil intent, a paraphrase but that's what it is like in practice). Moreover, even if you obtain punitive damages, they are very difficult to hold onto on appeal. (They are often reversed.)
I also do not understand the claim that Texas has "passed statutes which entice claims that are very lucrative to Plaintiffs." Texas is one of the most hostile states in the country toward's Plaintiff's claims and has led the way in tort reform.
I can also say that any decent plaintiff lawyer has zero fear of going against insurance lawyers. Just as there is a wide variety of talent in the local bar, there is a wide variety of talent in the insurance defense bar. As far as I'm aware, the insurance defense bar does not hold some vaunted reputation in the legal community.
I can say with absolute certainty that any decent plaintiff lawyer will prefer to go after an insurance company, not an individual. It's really hard to collect in Texas and insurance companies at least understand the game of litigation.
Finally, I'm not sure I understand the issue of fraud. What are you doing to get sued for fraud? Sure, anyone can sue anyone for "fraud," but in my experience frivolous claims get weeded out relatively quickly and certainly do not expose a defendant to catastrophic liability.
These are just some thoughts off the top of my head.