I have no insight why the roots in the buckets seem happier than the ones in the pots. Perhaps an oxygen exchange-balance thing, or an inherent need to go deep for nutes before it's competitors do, (in the wild) but I don't know.

There are three primary functions of roots:
1) to anchor the plant to a substrate
2) to absorb water and dissolved minerals, and
3) to store food reserves.
Info about roots

But there are specialty roots and membranes. All need water to dissolve the minerals, nutrients and/or gasses (air) in the soil it's in contact with.