I use my first three fingers and I don't have a problem.
While there are times that using the index barre is helpful, as when you want to stretch your pinky out to the A note at the 5th fret on the high E string, the traditional form is much more versatile.
For instance, it is very common to pick up both your index and middle fingers while still fretting the D note on the B string for a G6 chord. This is used in literally thousands of songs.
D G6 D Dsus4 D
e----2m---0----2----3p---2--
b----3r---3r---3----3----3--
g----2i---0----2----2----2--
d----0----0----0----0----0--
a---------------------------
e---------------------------
You could do this with your index I suppose, but it would not have the same dynamics.
With all chords it is best to learn several ways to fret them.
If you know something better than Rock and Roll, I'd like to hear it - Jerry Lee Lewis