I like the Argentine system actually.
Round 1 - simultaneous all-party primary on the same ballot, candidates signify what party they're wanting to represent, whoever gets most votes in a party's primary represents that party in Round 2, a party to be on the Round 2 ballot has to meet a minimum threshold (in Argentina's case, 1.5 to 2 percent).
What you've described here is what's known as a "blanket primary". While it's definitely an interesting system, the Supreme Court of the United States has ruled that it violates the 1st Amendment (See:
California Democratic Party v. Jones).
Some similar alternatives that are permitted include the Top-Two Primary and the Top-Four primary (the latter being advocated by FairVote).
