Trump, Carson, and Cruz are basically the cancer eating away at the inside of the GOP, which effectively paralyzes its efficiency outside of local and state elections. The blowback of the 2008 elections is still alive and well, and its not stopping any time soon.
I'd say the cancer really set in in the 2004 election. Although the GOP has always attracted the evangelical vote, that was the first time that they became central to its campaign. Rove believed (correctly) that the GOP could win by simply mobilising the traditionally low-voting parts of its base, which included a large slice of evangelicals. The problem is, while it was a good strategy for winning a close election, it may turn out to have hobbled the party, since in contexts where turning out the base isn't enough, the party finds it really hard to move beyond that base, since any attempt to reach out to the centre is pretty much guaranteed to alienate a bunch of otherwise-locked-in-voters, but there is no guarantee that an equivalent number of centrist voters will join the fold - let alone a larger number. It's ironic that George W Bush is not particularly popular with Republicans right now, because whatever else you might say about him, he was (or rather, he and Rove were) excellent at winning elections.
Of course it's not quite that simple - notably in 2004 Rove had a mandate to pursue a new strategy because the party had a clear leader (at least in an electoral sense). Now, with every election beginning with a bunch of people contesting the leadership, their tactical plans for winning elections are necessarily subordinate to getting nominated. So even if some Republican did make the same calculation I've made above - and I'm sure somebody has, much as I dislike the Republicans, they have plenty of talented political analysts - the guy who wants to take the short-term risk for the long-term gain has to win a primary against at minimum half a dozen guys who want to double down on avoiding the short-term risk.
Another factor is the US electoral culture, and the relatively high rate of non-participation. In other Anglosphere countries, notably Canada, the UK and NZ, right wing politicians can confidently reach for the centre because non-voting is a relatively rare phenomenon, so the number of hard-right voters they lose with X moderate policy is likely to be lesser than the number of centre-right and centre voters they gain with it.