I always thought that in an Arch-Conservative world, moderates should flock to the LCS banner. This idea supports that dream.
Issues that are L+ already become too liberal to talk about when recruiting, and increase the difficulty to keep the subject interested.
If the reverse is true, then it plus the public opinion change pretty much fulfills how I would think moderates would react in an Arch-Conservative world.
However, with 365 days of liberal action and unlimited liberal action squads, public opinion is generally very malleable to the determined liberal's needs. So even having public opinion shift by 10 or more points upon the law change would be fairly easy for successful liberal squads to fix. Now, if the LCS recently almost got wiped out and currently consists of a solitary socially inept cripple, it might be a bit more permanent...
Perhaps what is missing from the public opinion mechanic is the public's desire for change. The current system measures how the public feels about a law. Perhaps adding the public's desire for change as a more static statistic might prevent the ping-ponging and the ease of pushing public opinion currently.
It is also more authentic to real life. Take discrimination against minorities for example: Most people when asked directly agree that discrimination is morally wrong. But few are willing to support any real measures to prevent it. Contrast that with abortion: Whenever either side in the debate gains enough support in their favor, laws change immediately. The only things that keep abortion laws static are the deadlock in public opinion and Roe v. Wade.