Jury trials involve a lot of time, costs, and uncertainty. Juries are human and their verdicts need not be rational.
For claims significantly less than the defendant's assets, if the defendant is likely to be found liable, they may need to pay the plaintiff's losses as well as lawyer and court costs; settling before court most likely reduces the cost and provides certainty. For the plaintiff, settling before court may reduce the award, but provides it faster and with certainty.
For claims larger than the defendant's assets, typical cases involve an insurance company and in some cases a trial award that's above policy limits may be payable the insurance company if a settlement offer below the limits was offered by the plaintiff and not accepted by the insurance company (keyword: excess judgement), but if the plaintiff is on their own they may not care one way or the other --- a settlement they can't pay might be the same as a judgement they can't pay, perhaps delay and hope is preferred, perhaps they may be able to negotiate a settlement that they can pay. For the plaintiff, if there's only $X from the defendant, using it on legal costs is a loss, so settlement is preferable, especially if there's a chance of the defendant making the assets unavailable.
The incentives for settlement aren't so much about what plaintiffs' lawyers or defendants' lawyers are up to, but about how courts operate. Certainly lawyers have some influence on operation of courts, but it's a big combination of things, and IMHO, it falls more under government policy than anything else. If courts were staffed such that you could reliably expect to take an injury case from complaint to judgement in 6 weeks, maybe more people would do it. Of course, that might require more omniscience than is possible.
