First, the oversupply of lawyers started in about 1990, so you will see no real change now, about 2 decades later. At the time I would agree there was an increase in the more borderline lawsuits (but not frivolous lawsuits -- lawyers get sanctioned for these, so they largely don't exist except the rare egregious case you might see on SDN), but now it's pretty much a status quo. Second, the change in billing structure isn't as widespread as you think -- billable hours still rule in most places. But I don't see how billing is going to affect medmal, because those cases were and still are contingency (doesn't matter what you bill, you get a percentage of the take), and never were handled by the large law firms in the first place. So I say you won't see any change from any supposed change in the law, number of lawyers, or law firm billing practices, much of which happened decades ago anyhow. You might see changes from various governmental action, such as tort law reform like they have in Texas. But I wouldn't be so sure about that.
There is very little evidence that the INSURANCE industry is ever going to be lowering their costs in response to things like this. This is the OTHER "bad guy" in these cases. And their goal is always to generate more income this year then last, which can't be done if they lower their premiums.
It's really a lot like the gasoline industry -- the US gas companies raise their prices and blame OPEC, and the insurance industry raises its prices and blames the lawyers. In either case the person raising the price might be the one bilking you, but has an easier to hate target to pawn off on you. In fact, doctors premiums have gone up far faster than any increase in lawsuits/liability, and even in years in which lawsuits/liability was down. And nobody expects premiums to come down based on merely addressing the lawyer aspects. If you aren't attacking the insurance industry -- the more direct source of costs, you aren't going to see any real results.