First, Taft would have had to get elected. He wasn’t a popular war hero, like Eisenhower, and would have been subject to low attacks from Democrats that didn’t affect Ike’s campaign.
Secondly, he would have had to win Congress. Taft didn’t have the coattails Eisenhower did. The Taft-Hartley Act was a big bugaboo for labor unions and they would have gone all out to beat Taft.
Third, if Taft tried to repeal the New Deal he would have lost some Republican votes in Congress and wouldn’t have picked up as many Southern Democrat votes as you think. At that time, Southern Democrats were “conservative” in terms of not wanting more big government, but not conservative in terms of wanting less government. They had been elected with FDR. They voted for him. Their constituents had voted for him. Were they really going to vote to repeal TVA, Social Security, the SEC, FDIC.
Fourth, Taft would have had to live. He didn’t last out the Summer of 53. Whether he knew it or not he was dying, so maybe Eisenhower did Taft and his family a favor.
Fifth, what does it really mean to repeal the New Deal?
You are correct when you state the labor unions would have fought Taft fiercely. However, the Taft-Hartley Act passed in 1947, with 106 out of 177 Democrats in the House, and 20 out of 42 Democrats in the Senate, plus almost all Republicans, overriding President Truman's veto.
As for the South, the liberal-conservative divide was inside the Democratic Party. Some Democrats, like Willis Robertson of Virginia, Sam Ervin of North Carolina, Strom Thurmond of South Carolina, and Coke Stevenson of Texas, were more conservative than many Republicans.
While alternative history is only speculation, the 1952 election was the best chance we had to overturn the overreach of the Federal government.