The era where bipartisanship was more common during the last three or so decades of the long post-WWII (through mid-1990s) realignment wasn't because of a stronger center, it was because a very similar distribution of viewpoints as today was distributed between parties who weren't clearly aligned against each other on the main axis between the major factions; so you had the same recognizable liberal and conservative factions, with “liberal Republicans” and “conservative Democrats” being substantial factions. Historically and structurally this is an aberrant situation, the parties tend to align against each other on the major ideological axis of divisions in the countries. But things got shook up by the New Deal (and later public welfare programs) and then a series of Civil Rights measures that didn't quite fit the existing partisan alignment, and they came hard and fast enough that it took an unusually long time for the new alignment to shake out...
Now, there is a broad disenfranchised group, but it's not mainly the “center”, it's a diverse group of people whose views fall in a variety of places not near the axis between the major parties; in a system which supported more viable parties having a meaningful role in the political systems, they’d be served by their own parties; as it is now they are either protest voting or voting with whichever major party seems least bad at the moment and not liking it much, and in many cases being hyper-targeted by propaganda from the other major parties side not aiming to engage their interest, but to alienate them from the major party closer to their interests (or electoral politics generally) as part of the zero-sum nature of the two-party system.
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