I have an ep. of T or C where they have a baby race. Each baby wore a shirt with a number, representing dollars, and that money would be split with the mothers. Obviously, the baby with the highest number had to cross first in order to win a fair amount of money. Unfortunately, none of these babies were in much of a mood to "race", some of them crying probably because they were scared of the live audience. Bob kept saying "please stop the babies from crying, that breaks my heart".
So, if anything, Bob seems uncomfy with infants. I do remember an ep. of TPIR where they had a young girl, probably related to someone on the staff, and Bob actually held her and didn't seem uncomfy. He was smiling, actually.
I do think that even the casual TPIR viewer noticed that Rod was suddenly not shown on camera. While Stan Blits doesn't address Rod not being shown on camera, he did say that the showcases were sort of "downplayed" because they felt Bob was entertaining enough and the length of the showcase skits was shortened to give Bob more time to interact with the contestants (I'm sure increasing commercial time is a factor as well)
I hope with Drew taking over, that perhaps the showcases can become more entertaining and wacky again. Considering that Drew has worked with ensembles in his own show and Whose Line, he doesn't seem to be afraid of being upstaged.