The true answer is of course it depends. What it depends on is how you define sustainability.
In a natural resources context, with weak sustainability, soil quality is a capital asset, just as a fish stock, a forest or an oil field. Given that we have manure and fertilizer I would argue that it is a renewable resource (until we run out of phosphate perhaps or poison the soil with too many pesticides), but let's start from the simpler case of a non-renewable resource.
In that case the golden rule tells us to gradually exhaust the soil until no more degradation is possible. In the simplest case we should degrade at the rate of interest. You correctly observed that in principle there are no externalities. The individual optimal solution is equal to the social optimal solution, provided the individual discount rate (interest rate) is equal to the social discount rate (see e.g. Clark 2010 for this often missed point).
One can modify such a model to allow for renewable resources with the use of fertilizer or natural regeneration, which would change the solution somewhat. Kenneth McConnel (1983) has a model showing the basics.
The reason that soil exhaustion is optimal is that the proceeds can be invested in alternative assets, which generate a larger rent. The problem is of course that i) this model assumes we discount the future (which we do) so future generations are discounted; ii) such models at an economy wide level typically assume the existence of a backstop technology, something we can use when we run out of good quality soil. Whether or not something like that will exist is debatable.
Moving towards a strong sustainability viewpoint the main thought is that we should not deplete our natural resources beyond their regenerative capacity, unless we already have a substitute. We don't currently have a real good substitute for soil quality, although we can use fertilizers and such to make up for some of that. From a strong sustainable perspective we are therefore not (yet) sustainable.
From a bit broader perspective the production of artificial fertilizer is very energy intensive, and one can question whether the current amounts used (as well as the earlier mentioned pesticides) do not have unintended effects, but then you're back at externalities.