which 6 from Party A and which 4 from Party B win matters far less than how many As vs Bs get seats
Valid point. So choose your registration carefully.
the guy who bribes or coerces you to register with Party A controls that.
I have never seen any bribery going on. So not worried about it. ... Yet.
You haven't seen it because it's not happening much. But it's precisely because the decisive choice is made in secret that bribery isn't going on -- there's nothing to stop you from taking the money in return for your promise to vote for A and then voting for B in the privacy of the voting booth. That kills the incentive for anyone to bribe you. The same goes for intimidation. Secret ballots were adopted in the late 1800s, not because people philosophically felt it was a good idea, but in reaction to the constant vote-buying and coercion of the era. If we move the decisive choice from the private part of the process to the public part then we'll bring the incentive back, and that will probably bring the vote-buying and intimidation back.
There's a god web-page on the history here:
How the Secret Ballot Ended the Gilded Age
"Beginning in the 1830s, the iconic symbol of democracy — as depicted below in engravings and photographs — was the transparent glass globe ballot box. Voting was public, visible, and deliberately exposed. By the late nineteenth century, however, as partisanship intensified and campaign finance and economic inequality soared to historic highs, the United States shifted decisively toward increasingly stringent forms of the secret ballot - leading to the introduction of the Australian ballot. The intentions were explicit. From the labor movement to the Chartists, reformers argued that secrecy would blunt the power of intimidating landlords and disrupt the rampant vote-buying and coercion financed by wealthy interests. The secret ballot was designed not as a cosmetic reform, but as a structural defense against the ‘undue influence of wealth’ via intimidation and purchased loyalty. ..."
(Ironically, the glass globe itself had been a reform, designed to protect against an earlier period's prevailing form of election corruption: ballot-box stuffing. Election security is an arms race.)