The problem of a stronger Socialist Party under Asanuma causing even more American interfering could lead to a more competative system down the line, albeit with cost. Here's my back of a fag packet scenario:
Say you have Asanuma leading a growing 'red wave' of popular support for the JSP in the early 1960s. He survives the assassination attempt, only upping his street cred. The CIA nudges Kennedy but he pays little heed, not keen on undermining democracy in an allied former Axis Power. This leads to a position were Asanuma has an outside chance of winning an upcoming election. The zaibatsu and other interested groups are giving the Americans nervous glances. Hung election, JSP the largest party, pro-Asanuma protests, increasing labour unrest.
By this point LBJ is in charge (assume JFK still assassinated) and the situation is more serious. He has some discussions with John McCone. McCone doesn't have the Cold Warrior reputation of his predeccessor Dulles but in less than four years he oversaw coups in the Dominican Republic, Brazil, Ecuador and Guyana, not to mention arming the Hmong in Laos. His part in the Cuban Missile Crisis and opposition to overthrowing Diem have earned him retrospective brownie points but he was as into Domino Theory as anyone.
Launching a coup in 1960s Japan, even a bloodless internal coup, no doubt has many implications I'm not educated on frankly, the role of the JSDF being the biggun'. However if the CIA can lend a hand in establishing an emergency non-socialist government (arrest Diet members, leaving a rump?) it will cause untold butterflies. I'm not informed enough to how authoritarian or permanent such a regime could be, but you'll have the Liberal-Democrats culpable to some extent and when its over, probably a lot of citizens very keen not to have it happen again.
This leads to a post-JSP party (called something uncontroversial like Progressives or whatever) taking power and instituting reforms to the post-war system, including a more open, proportional electoral system.