He did. Eisenhower was the epitome of a moderate Republican. The tax rates during the Eisenhower administration was at an all-time high. He did nothing about the emerging welfare state.
But...as I've stated Eisenhower can be excused because of his military service, and to a lesser extent, he deported the illegal aliens.
Eisenhower campaigned on conservative themes in 1952, but when he got in, he governed as a moderate. Just as in 1968, Nixon campaigned as the champion of the “forgotten man,” the hard-pressed Middle American from flyover country, then swung hard left once he made it to the White House.