Why not for the index tab? There's no other appropriate place to put input focus. In fact if you put the I-beam there, leave the keyword index, and return to the keyword index, the insertion point is still there ... ought to be easy.
"... can bear to touch your mouse [one more time]"
Yes, but when you first go to the keyword index the input focus is nowhere. I can't think of a better (more likely to be used) place than the edit control. Its being there has no effect on the other things you might do.