Learning theory says that some tasks you learn first help with later tasks. However, there are some tasks you learn first which interfere with later tasks.
Had you learned a later task first, it would not have interfered with the first task, and perhaps might have made it easier to learn that first task. Not mumbo-jumbo, but something to consider for learners of any age: I have yet to see the 0-0-0-3 chord taught with the little finger. It is (3) on the chart. That is the ring finger.
The 2-0-1-0 chord is taught as (2) x (1) for fingers. It is just as easy to finger it
as (3) x (2). The 0-2-1-2 chord is taught as x (2) (1) (3). It is actually easier to play it as x (3) (2) (4). Those three chords are moveable chords shapes. The most common way to easily play an {Amajor for dgbe tuning} Dmajor for GCEA tuning, is 2-2-2-5. Try to reach that 5th fret with the ring finger.
The #4 finger reaches it easily. Initially learning to have the index finger dedicated as a barre does not make it necessary to learn another set of fingerings to play those chord shapes at another position on the fret board.
Yes, barring is difficult, and may be a year or so down the road before they do it successfully, but the fingering pattern will make it easier, and all that is different is how to use the first finger. There are other chord which can easily be made without the use of the first finger. 1-2-0-2 is another one which is a moveable chord shape. If it is learned as (2) (3) x (4), the #1 finger is free to fill in that x string anywhere it will be played on up the neck.
Complicated? Only because of our having learned it the other way. To those who learn as suggested here, the chord shape does not require one fingering pattern in the first and second fret chords and a different set of fingering patterns for that same shape when played higher up the neck. Teach for not just the here and now, but lay a groundwork which will make going on not be a conflict of which fingers to use. I would suggest you make up fingering positions different from what shows a heavy dependency on the index finger in the first and second fret range