When you say "more useful": To who? In what context? To achieve what ends?
There is no sense or benefit in pushing at a "pull" door, for instance.
You're right; it's basically replacing one vague term with another one.
Te is "useful" in the sense that it tries to work efficiently within a given system, or "play the system" if you will, whereas Ti is probably more concerned with establishing an efficient system in the first place.
Efficient in the sense of getting things done with minimal effort (in the most basic, general sense). Of course Te can also be concerned with establishing an efficient system, but only as a means to an end.
E.g.: Ti: That door is poorly constructed, I could make a better one. Te: I pull at the knob instead of sucking at the door with my mouth and moving backwards to open it because using the knob is the easiest way to open a door. Or something like that.
Anyway, this thread is still vague. I'd rather debate within given definitions of Ti/Te instead of establishing and discussing definitions/explanations of functions and their usefulness (or "betterness") by the posters themselves.