First, of all, did Thomas travel to Nashville over the same route as Schofield? If he did not how was he to know the bridge at Franklin was missing?
Second, as stated by Schofield, he had no intention of fighting for Franklin at all. He had just escaped disaster at Spring Hill and was high-tailing it to Thomas as soon as he possibly could. Thomas had no need to reinforce Schofield to defend Franklin, because he no intention of defending it(despite Thomas' request to do so if he could)
Third, Hood attacked prematurely because even as his Army was arriving at Franklin, he could see that the bridge had been repaired and the Union forces were already crossing the river, even as he watched. If Schofield's retreat was to be stopped, he had to attack immediately. If Hood wanted Franklin, he could had it for nothing in a few hours...if that was what he wanted.
As already noted, it is a false assumption that Thomas inherited a field army ready for active campaigning at Nashville. Schofield's force was to be the solid vertran core of the Army that Thomas was in the process of forming,