I really like this idea - it's quite original and has lots of merit.
However, there are a few problems. The most obvious of which being the inability to finalise a season winner with any real fairness. I like the idea that New South Wales or Central Districts can win the First Class competition in season X overall, and I wouldn't like to see that removed. Unless you actually had a three-match home series and a three-match away series against each team, which would take up more time than a cricket season allows, this wouldn't really be possible. Even if that somehow was arranged, you could theoretically have a conflict between the interests of the series and the interests of the championship for a team (ie. up 1-0 after two games, needing to win the third to make the championship final but only needing to draw it to win the series, chasing a possible yet unlikely target in the last 4 sessions). There are probably more problems I haven't actually thought of, as well.
I certainly wouldn't be violently opposed to it, but I wouldn't be implementing it if I had the choice at this stage.