Louisiana has had this system since 1975. For years, Democrats faced other Democrats in general elections; this is now much less likely to occur except in Democrat rotten boroughs. All of CA nearly meets the definition of a “rotten borough”.
And in many instances, it does not benefit Conservatives. If you end up with two leftist Democrats, Republicans have no choice, but if you end up with two Republicans, almost always the more left-leaning one wins (with Dems providing the margin of victory). Only in the LA Atty Gen race did the more Conservative Republican (Landry) prevail over the ex-Democrat turned Republican (Caldwell).
What are you talking about?
“A rotten or pocket borough, more formally known as a nomination borough or proprietarial borough, was a parliamentary borough or constituency in England, Great Britain, and the United Kingdom in existence prior to the Reform Act 1832 which had a very small electorate and could be used by a patron to gain unrepresentative influence within the Unreformed House of Commons.”