There has been a slow overall trend around the world to make elections more democratic that has been going on for about 200 years. Many countries changed election laws over the decades to keep up with this (allowing women to vote, allowing 18 year olds to vote, limiting donations, changing the electoral system to make the outcomes more representative to how people actually voted, etc).
In the US this took the form of both parties opening up their candidate nomination process to the wider membership of their party. Now the party bigwigs—the insiders—no longer solely decided who would be selected to stand for each party. This eventually progressed so far that in many states anyone can vote for who the Dem or Rep nominee will be, even if they are a member of the opposite party.
This fulfilled the societal "urge" for greater democracy, but it also brought about serious problems; because the quickest route to success for a politician is to stand for nomination of one of the two parties, even if your politics are quite different from that party's mainstream (think Bernie or Trump in 2015 versus Clinton or Bush). There is now no incentive to start a third party, that will struggle for decades before it can start to get some real power in government (it often takes third parties in other countries, even with proportional systems, decades to get cabinet postions).
So starting a third party is much less attractive than just taking over an existing party via the open nomination process.
A huge downside of this however is that each party's nomination (primary) election becomes a contest between the extreme and moderate factions of the party and because you only have to convince your own party's voters at this stage the extreme candidate often wins and becomes the new face of that party. The more extreme the winning nominees are the greater the incentive for the other side to vote against the opponent, even if they don't like their own guy that much.
In the end this is a positive feedback loop where each party becomes more extreme over time and it becomes much harder to justify voting for a third party.