Roots head for moisture not walls. If you want a plant with deep roots, you water deeply and allow to dry before watering again. This trains the roots to grow towards the water so it will have the ability to access water way below the surface, thus drought tolerant/resistant.
The most important reason to maintain pot size to the plant size is water/moisture. A pot that is correct to the plant size will have room to grow roots that suck up the moisture...more importantly there is no excess water and subsequent root rot. You do not want water staying in the soil, in a saucer, unless you have a semi aquatic plant.
Another thing most people do not realize is that transplanting and 'fruffing' up the roots (slightly breaking and interrupting any circling of the roots) causes MORE and healthy root growth to fill the new pot. Babying roots is not a good thing.
And another thing about potted plants that most people do not understand is the roots maintain a certain amount of canopy or photosynthetic growth. If the photosynthetic growth is larger than the root mass, this would necessitate pruning the above surface growth to match. If the root mass is larger than the photosynthetic above surface growth, again, the roots would need pruning to match the 'food making factory'. Storage and uptake (roots) have to match the food factories (top growth, photosynthetic). Or the plant will be majorly stressed.
Planting in a pot that matches the plant keeps this relationship in order. Small plant, small roots, small pot. Large plant, large root mass, large pot. Too many people jump to the conclusion that a small plant should be planted in a large pot that it would/should inhabit once mature and seems so much EASIER. WRONGO!! Not only does a too small plant in a too large pot puts the plant at risk of root rot, fungal diseases, it also slows the growth WAY DOWN. The roots are furiously trying to make sense of the amount of soil and are putting more energy into root building than vegetative growth (not to mention reproductive growth).
Do not try to correlate any of this to plants planted in the garden soil...potted plants are 100 percent dependent on their stewards. Totally different situations; pots versus garden plants!