A little more info.
https://www.jmoreyins.com/2013/03/15/carpool_lane_yellow_white_lines_meaning/
This only partially answered my question. It states that crossing the solid yellows are not allowed, but it still did not tell me why the white line was there. It took some more research but I found that according to the California Manual on Uniform Traffic Control Devices (MUTCD) Section 3B.04, a solid white line means that crossing it is discouraged, but not illegal. Some examples of this would be seen on one-way streets or just before an intersection. If the conditions are right and you can change lanes safely, go ahead.
However, the carpool lane is an exception. The white line in this case, is there as a lane barrier and should not be crossed until there is a designated entry/exit place marked by broken lines.