Eliminate is in effect treating other variables as ones to solve for, and using polynomial algebra to eliminate T from the set of "polynomialized" expressions. In this last case it is apparently hitting some serious complexity in trying to compute a Groebner basis for the task at hand.
Stated differently, the function is nowhere near as smart as you think. A possible future task would be to recognize the special case where the elimination variables only appear linearly with respect to one another.
