I think this says more about how much harder it is for liberal Republicans to rebuild their career after leaving their party than it is for conservative Democrats.
The success rate for conservative Democrats who became Republicans is a lot higher in terms of staying in office and/or moving on to higher offices. Louisiana is basically run by former conservative Democrats; so is Georgia. Mississippi, Alabama and Oklahoma have plenty of them in their state houses too.
But if you go to New England or the West Coast or other places where liberal and moderate Republicans were a dime a dozen 50 years ago, they're not still around existing as Democrats. They usually stay with their party and retire or get defeated for reelection. If they do leave, it's to become an independent (Lowell Weicker, Jim Jeffords) and usually they can manage to win one election that way.
But the liberal Republicans who become Democrats have always fallen flat. John Lindsay's spectacularly bad tenure as the Liberal/Democratic Mayor of New York is the worst case I can think of. Ogden Reid's career basically ended after he left the GOP. Add Lincoln Chafee to the list.
Not too surprising. In many Southern states (especially - in DEEP South) there was virtually no Republican party before an exodus of conservative Democrats from their "new", more liberal, Democratic party. So, there was, virtually, almost no intraparty competition for influence and power (there were some exceptions, like Holshouser-Gardner governor primary in 1972 in North Carolina, but that's an exception caused by existence of "old Mountain Republicanism" in Virginia, North Carolina and Tennessee). On the contrary, most of the North-Eastern states, where moderate-to-liberal Republicans migrated to Democratic party, had vibrant Democratic party
before that, so competition was fierce, and, thus, the transition went much less smoothly.
