If you have assets, protect them. However, if you ever need it, know that once the lawyers find out you have one, it will be blood in the water.
Actually, it's chum to distract them from your assets to the Insurer's, and they're usually already hungry enough to bite and eat whatever is in the water. With high limits, a settlement is FAR more likely. When there is too little in your policies to pay something close to the value of a case without going after the defendant's assets directly, the plaintiff's shark will be coming for your assets. You are then trying to keep your insurer in the lawsuit, defending pursuant to its duty in the policy to defend, while it is claiming that its duty should not go on indefinitely when you have a $750,000 case against you, only $50,000 in insurance, and little to no chance for that clear liability rear ender when you blew a .09. If you have $1,000,000 in insurance, there's a much better chance that the plaintiff's shark will try to get his client and himself paid and go away, and that your insurer's obligation to indemnify is high enough $$ that they won't be trying to cut and run on declaratory relief.
If the plaintiff's shark knows what he is doing and there's a decent sized policy, he'll fully inform his client about this strategy, and with client consent, make a demand on your insurer for the policy limit (or less). Why? Because if the insurer doesn't settle it when it had a chance for an amount within the policy limit, and the plaintiff's shark thereafter gets a judgment against you for an amount above the policy limits, you have a bad faith case** against your insurer for the excess amount (and some other damages that are not assignable). But what's important is that the "excess judgment" (difference between judgment and policy limit) is usually something you can assign to the plaintiff (in a post judgment settlement) in exchange for a release from liability for more than the policy. (So, the plaintiff has ready insurer money from which to satisfy the judgment beyond the policy limit in that case, rather than trying to wring it out of you.) Too low a policy and the plaintiff's shark will not be making a policy limits (or less) demand, but even if a case is potentially a really big one, a plaintiff's attorney will be motivated by his split on a healthy policy limits setlement, AND in any event, he has an obligation to tell the client that a judgment is still a crap shoot, may take years to finally get paid on, and that it's usually cheaper (in attorney fees and costs that come out of the recovery) to settle than to go to trial and through the likely appeal. A bird in the hand, you know. OTOH, low limits seldom make the sharks go away unless you really don't have squat to go after, including no reasonably remunerative employment. Pay the money on the premiums for the peace of mind and likely shorter involvement in teh painful process of getting sued.
**In California, this is the Johansen case -- insurer breached its fiduciary duty and its duty of good faith and fair dealing to its insured by failing to settle for an amount within policy limit when it had the chance, thus exposing insured's assets to risk on the amount of the judgment above the policy limits. The judgment serves as proof of the true value of the case against the insured. In other words, the insurer tried to save itself some money by putting its insured at risk, which a fiduciary may not do. So, the court shifted the risk of doing that to the insurer -- if they want to play hard ball in negotiations, that's fine, but they do so at their risk, not their insured's.
