The diffraction-limited field in a newtonian is actually quite small so objects are sharper in the center of the FOV. This has nothing to do with eyepieces, though good ones like Naglers will have less astigmatism (seagulls at the edges) which is another problem.
For visual observing, ultimately the discernment of detail is made by the human brain, so it is not unreasonable to suggest that it will notice greater detail if it it is more relaxed and not using some thinking processes for nudging the scope.
These problems are more of an issue at higher powers when objects whizz across the field quickly. One thing a larger scope allows you to do because of it's greater light grasp is to increase the magnification on small, faint objects like planetaries and galaxies without them dimming too much. It also has greater resolution and thus potential, when the atmosphere allows, to increase the magnification more than a smaller scope. So the bigger the scope, the more advantageous tracking becomes.
Many experienced observers have stated there is an increase in the discernment of detail by adding tracking to a large newtonian, not unlike an increase in aperture. There is, of course, no more detail collected by the telescope but the person viewing does indeed see a bit more IMO.
Anyway, it's nice to have but not essential for enjoyable viewing (a relief given the plunging Aussie dollar) and probably goes against the low-tech, low-cost, no-fuss, yogurt-powered Dobsonian ethos somewhat.