There is been some noise across the internet after California voters passed Prop 14, which creates a blanket primary system (some people call this a open primary, but it is not an open primary; the appropriate name is a blanket primary or top-two primary) similar to those used by Louisiana and once used by Washington State:
As this system is essentially like our current special elections in Texas, I don't see this reducing the partisanship or polarization in the Texas Legislature (and there is no evidence that it has anywhere else either), and there are better ways to increase voter turnout.
Some more resources on this issue:
The Vanishing Voter by Thomas Patterson
Fixing Elections by Steven Hill