No, because I do not think that this is the best manner in which to address the issue. I favor a ballot in which you receive the parties side by side and must choose which party to vote in each race, allowing for switching between races.
I'm pretty sure this has been floated, but I don't remember the name of it.
I have always favored this method, but it became even more important to me when last Spring I took a Republican ballot just for the honor to vote for my GOP state rep who voted for same-sex marriage in the IL house. I helped him fend off his social conservative hack challenger handily.
The problem with this type of open primary is that it infringes on the parties freedom of association. A traditional open primary (like in IL) allows voters to choose which party to associate with on election day, and they may change it at the next election. Some states have ruled that a fully open primary goes too far and instead support a closed primary where partisan declarations are made in advance of the primary, or in some states the parties are allowed to separately choose the form (one open, one closed).
The top-two or blanket primary avoids the association problem by completely eliminating partisan primaries. Association can be accomplished by candidates stating their party preference, though that is not necessary to the blanket primary model.