Is it that unusual? LDP is a conservative party that holds a majority with the voting public, and the opposition to conservatives everywhere is often much more fractured.
Seeing it from the outside, the LDP seems like Japan's Republican party, Komeito is the Evangelical Christian bloc, and Abe is your basic Conservative running on American exceptionalism and traditional cultural values.
The biggest obvious difference is the failure of the LDP to successfully repeal Article 9, but as I understand it, that doesn't have nearly as much popular support in Japan as war posturing does in the US.
Britain lurched to the right after Margaret Thatcher but that didn't keep Labor from being in power for a few years (by co-opting the Tory program the same way Clinton co-opted Reagan) Germany, Israel, France, and numerous countries with parliamentary systems have power alternate between parties.
As for "opposition to conservatives everywhere is often much more fractured" that makes me think of an observation I've had which is that conservatives in the US are united by the idea that there is a way that things are "spozed" to be whereas what passes for the left in the US are a groups of people who perceive themselves to either be outgroups or be supportive of outgroups. The problem is that racial/ethnic groups such as blacks or latinos don't automatically support, say, transsexual maximalism. Environmentalism is still perceived as a "white thing" even though blacks are worse off when it comes to exposure to toxics. "Environmental racism" as an issue just hasn't sold.
