CT Republicans have already tried it.

Recently former Secretary of State Pauline Kezer suggested we allow unaffiliated voters to vote in primaries.

We tried that and it created a disaster.

This was originally posted on August 17th 2006 at another site:
http://connecticutlocalpolitics.blogspot.com/2006/08/lieberman-rell-with-large-leads.html

Dick Bozzuto

English as a 2nd language, self made man (people confuse him with his now late half-brother, Adam the IGA mogul who was also a wonderful man) drop dead straight, ethics and behavior beyond reproach.

Moderate Republican, before the word got ruined it was "Progressive" Republican he was/is a populist.

Former CT state senator. 

Ran for senate in 1980; got beat by a carpetbagging ultra-conservative named Buckley who in turn lost miserably.

Had the 82 Gov nomination sewn up when convention chair Larry DeNardis allowed the convention rules to be broken by Labriola & Rome; they had a love-fest and there was as a result no 2nd roll call.

Bozzuto had 49.7 % of that convention. 

At the same convention Prescott Bush Jr had challanged Weicker had received around 24% (??) of the vote more than enough to primary.

Lowell didn't like that and called Dick to get his delegates to back his hair-brained idea to allow ind. to vote in state wide GOP primaries in case it ever happened again. 
For this Lowell is 100% behind Dick in 86.
They shake on it.

We all held our noses, took a stiff drink and did so at a special rules convention.
(I was at all these things)

1986 - Lowell rolls out Julie Belaga who barely gets enough votes to primary. 
Weickers people start up the "in the Mafia" nonsense against Dick (as if every Italian with 3 bucks is a hood).

There's Richard C. Bozzuto, the literal personification as to what is right and good about our nation and state and these disgusting people had the nerve to smear his good family name?
IT WAS TRULY HORRIBLE.

Sept. 9th 1986 - with an astonishing number of poll workers (same way Weicker won Gov in 1990) Belaga beats Bozzuto the GOP convention nominee.

Nov. 1986 - worst defeat in the history of the Republican Party in CT.

Dick had used his popularity and whatever celebrity he might have enjoyed to the benefit of others including myself, tirelessly and liberally. He would show up for a function anywhere in CT if one of his supporters thought it might help him or her win a few votes for Planning & Zoning, Alderman, Town Council, or Dog Catcher. He went door to door with me and spoke Italian to voters who clearly adored him and he certainly didn't do me any damage in doing so either. (I'm a WASP)
Dick was the most loyal ranking Republican I ever had the honor to associate with in my life.

Many single words could be used to describe him, including; Good, fair, honest, but the one overwhelming characteristic he still enjoys is kind. The man is kind to fault even eclipsing the one thing upon which he most prides himself - loyal.

Were we to drag him (kicking and screaming I'm quite sure) back into the game he would light a fire; the man can really speak and has some other quality that maybe someone with a high degree in English might be able to quantify in words but I can't. But I would to this day go though a wall for him, or for that matter follow him into the gates of hell and I'd assume we were going to come back victorious.