@Filippo - 'replaced by something absolutely identical'....I think not
Not sure why you think that. Parties have changed positions over the years. Prior to WW II, the republican party was very isolationist and very much against increases in military spending. They did not support the US getting involved in WW II by helping the British or Chinese against their respective foes. While the democratic party wasn't exactly the opposite, they were not nearly so isolationist and mostly supported increased military spending and military aid for those fighting the Axis powers.
By the 80s, the republican party was very much for increases in military spending and pro engagement in the world, while the democrats mostly did not support increased military spending and had a large anti-war contingent thanks to the failure of the Vietnam war which they were mostly responsible for getting the US embroiled in.
It wasn't until the 60s that the republican party started to actively court what is now known as the "religious right" and completely dictates their social policy platform.
One can even look today, and the positions Trump campaigned on to find a few that are widely divergent from that of republicans even two years ago. Republicans have long been in favor of free trade agreements like NAFTA and TPP, but Trump has if not completely changed their direction at least has a large rudder in the water making a U-turn. They were always the more anti-communist party, and even after the USSR fell have remained highly suspicious of Russia and their motives. Trump treats them like his best friends, and while he will openly criticize the leaders of long time allies like the UK, France and Germany, he has never said anything bad about Russia or its leader.
So I'm not sure why you think that if the two parties had their national structure effectively undone for an election cycle or two that they would emerge with the same positions. The 'new' republican party might end up as anti-free trade, or even isolationist. If the party fractured on a national level and it was left to state organizations to build it back up again, look at which states are the biggest, and their social views versus current party platforms? It might not follow the religious right quite so much in things like gay marriage and transgender rights - after all, where are those social conservatives going to go, the democratic party?
Likewise the democrats may turn back the clock on the changes Bill Clinton made to the party in the 90s by supporting free trade and Wall Street and return to the more populist positions on those issues they held prior to Clinton's presidency that Bernie was pretty successfully campaigning on. There has been some grassroots movements in some states for democrats to try to include the so-called "religious left" who have been largely absent from politics, by framing issues of helping the less fortunate in society with religious messages like "what would Jesus do?"