I definitely agree with your main point, that people should be able to cross over and vote in multiple parties' primaries. Maybe even in a ranked-choice style?

I remember, during the 2012 presidential primary, I voted for Jon Hunstman (even though I'd supported Bill Richardson in the 2008 primaries, and then Obama in the '08 General Election), because he was the only Republican running that year who was sane and rational, in my view.

Then, when Romney won the nomination, I turned right around and voted to reelect Obama, despite my dissatisfaction with him (I was *THIS CLOSE* to voting for Gary Johnson in the 2012 General Election; it wasn't until 2016 when I became educated about Johnson's ill-conceived support for the so-called "FairTax"...)