and it's not like an xxTP ONLY has Ti. they have all the other judging functions, too, to some degree.
from the Pi's perspective, the values aren't even decipherable. it's the F function's job to decipher them and analyze them against other data from P functions.
all judging functions function the same exact way. pure deduction. the information they deduce from is what's different.
J functions don't start with any information by themselves. they get information from P functions and output the result of their analysis.
to me, it doesn't make sense any other way.