I'm not convinced the premise of the question is true with regard to centrist governments, at least in the post-World War II era. There have been center-left, center-right coalitions in all of Europe's largest countries, for example, in the last 75 years.
Italy, for example, had various permutations of the five most centrist political parties in the country, the Pentapartito, in short lived government coalitions that not infrequently crossed center-left to center-right lines for decades, often re-forming almost identical government coalitions after elections held not long after previous elections failed to resolve deadlocks that arose in previous coalitions.
The United Kingdom famously had a "grand coalition" and skipped an election that otherwise would have been required since more than five years elapsed from the previous election, during World War II. See also the unity government of Belgium in 1946, and Canada in 1917.
Grand coalitions of center-left and center-right parties were formed in Germany following elections in 2005 and 2013, and West Germany had a grand coalition government following elections in 1966.
It is hardly surprising that far-left and far-right parties are rarely found in the same coalition. They have little or no policy common ground upon which to cooperate in a coalition forming a government.
It isn't clear how you count a minority government in a parliamentary system, such as Australia after the 2010 election, Belgium in 1958 and 2020, fifteen times in Canada (most recently in 2021), Denmark (frequently from 1982 through 2019), six times in Estonia since 1992 (most recently in 2018), several times in Germany, eleven times in Ireland (most recently in 2016), in the Netherlands in two governments from 2010 to 2017, in Norway in 2013 and 2020, in Sweden many times including a center-left/center-right minority government in 2010 and a current left leaning minority government, in the U.K. briefly in 2017, and currently also in Croatia, Israel, Poland, Slovenia and Spain.
And, it is trivially true that every time you don't have either a far-left/far-right coalition, a centrist grand coalition, or divided government (in countries like the U.S. and France, where this is possible and not terribly uncommon, and there have also been minority governments which are a close analog of divided governments in countries where truly divided government is structurally more or less forbidden), you have either a center-left and left coalition for a while, and then a center-right and right coalition, or visa versa, since those are the only remaining permutations and seem to be within the meaning of what the OP calls a "rotation" even though the transitions from left to right and back again, don't always follow one after the other.
Further, simply putting coalitions into a left leaning, right leaning, or grant box, when there isn't divided government, can conceal the fairly rare, but important complete restructuring of political parties on one side or the other of the political spectrum.
For example, the landscape of political parties in Canada profoundly changed between 2004 and 2011, despite the overall left-right balance not changing all that much.
Italy eventually broke out of being stock in its Pentapartito politics after constitutional reforms were adopted and new parties were formed.
Mexico, after about a century broke out of a PRI dominant party system into a system with competitive parties with real viability.
The Republican Party in the U.S. arose from the collapse of Northern Liberal establishment parties shortly before the U.S. Civil War.
This list is certainly not exhaustive.
So, there is infrequent but dramatic change in the lineup of political parties every now and then which simple left-right boxes don't capture.