In essence, these firms have enough billings to pay for certain of their attorneys to participate in local, state, and national bar association activities and on judicial nominating commissions. In this manner, these firms get enough clout among the judges to have the benefit of the doubt or outright political sway to rig a case when they need to.
More broadly, the effect is to screen against untrusted outsiders and keep them off the bench. Yet such outsiders often have greater honesty and dedication to deciding cases on the merits than insiders compromised by their affiliations.
In addition, the process also tends to empower Leftists who might otherwise generate political heat against the coziness of the system. In return for supporting the judicial influence game, the Leftists work to keep conservatives from getting on the bench.
Thank you for your very good explanation of how these things work.