Ummm...no. The Republican party bosses who controlled the delegates wanted Taft.
The primary vote was a pretty new thing back then, and did not control the delegates as it does today. Roosevelt beat Taft in the 1912 primary vote by about 500,000 votes total, handily kicking Taft's butt even in his home state of Ohio.
But the nomination was given to Taft in the smoky back-rooms because the primary popular vote was non-binding. This is why Roosevelt bolted the party and ran on the 'Bull-Moose' ticket.
When the Republicans made overtures to Roosevelt about supporting him in 1916 if he wouldn't run as a third-party candidate in 1912, he famously commented:
"A homily on honesty, given by a thief who refuses to give back that which he has stolen, does not tend to edification."
*LOL* It is my favorite TR quote (and boy he left us a bushel of them!)
However, those reforms were necessary and, had they been enacted in the 1912 time frame, would have been far more moderate than the ones undertaken by FDR during the Depression.
Roosevelt pretty much had the GOP nomination sewn up for 1920 due to his tireless advocacy of Americanism and the Allied cause in WWI, years before Wilson flip-flopped and took us to war.
It was TR who would have been elected in 1920 instead of Harding, had he lived (he died in January 1919 at the age of 60, partly from the accumulation of diseases and injuries suffered during his tumultuous life - his expedition to the Matto Grosso in South America in 1914(I believe) being particularly harmful to his health as he nearly died from tropical fever and lost about 70 pounds at that time - and partly from a broken heart following his youngest son Quentin's death in a dogfight over France six months). earlier).
And, I have always held, that HAD TR been president from 1920-28, history might have been very different, particularly as needed reforms would have been implemented and thus the catastrophy of the Great Depression lessened or avoided altogether.....