There are several issues with that. The largest one is that you assert that the costs can only inflate. They cannot.
TL;DR – Yes, but the added value gets smaller each recursion, such that even if you add on an infinite amount of these costs it will only come out to a finite value. The productivity of a single person, which in today's industrial world is immense, makes these costs so small they might as well be cents on the final product.
Let's say a farmer farms a square field with 100 metre sides, or exactly 1 ha of land. This is a size which it is perfectly reasonable for one person to farm, even entirely by hand, and which is woefully small considering modern farming equipment. On it they grow wheat, with a production of 0.25 kg/m² annually, or 2 500 kg when you do the calculation. This is a perfectly reasonable yield. Taking into account milling yield, we end up with only about 70% of that, or 1 750 kg of flour. A loaf takes roughly half a kilo of flour so, assuming water and yeast are effectively free, so selling this to a baker, they produce 3 500 loaves in the end.
So far, so easy. Then we take into account the losses that are going to be accrued for the loaf of a single customer in this very small thought experiment economy, in which exist only the farmer and the baker. Each, we say, might eat 2 entire half-kilogram loaves in a week, so 8 in a month and 96 in a year. The baker prices one loaf at (flour cost + 96·loaf cost)/3 500. The farmer prices his flour at 96·loaf cost/1 750 kg, but as the farmer buys everything, we can ignore the division. The price of one loaf is now (96·loaf cost + 96·loaf cost)/3 500, or 192·loaf cost/3500, or, rounding a bit, 0.05·loaf cost. Propagating it down, we have 0.05²·loaf cost, then 0.05³·loaf cost, and when you recurse to infinity, we have 0. The further you get from the producer, the smaller the added cost becomes in reality, such that even if you add up all the costs you eventually reach not an infinite value but a finite one.
If we say that each take a profit of $100 annually in addition to what they need to live, we get that the farmer prices their flour at ($100 + 96·loaf cost)/1 750 kg and the baker their bread at ($200 + 192·loaf cost)/3 500. Propagating it down, the price becomes ($200 + 192·($0.06 + 0.05·loaf cost))/3500 = ($210 + 0.05·loaf cost)/3 500. Going further, it will be ($210 + 0.05·($0.06 + 1.4·10⁻⁵·loaf cost))/3 500 where we entirely lose precision and the added cost from profits appears to stay at $210/3 500, while the rest of the calculation becomes so small it disappears off to 0 at infinity once again.
While this example is only very simple, and I won't prove here that it applies in larger or more complex cycles, it is nevertheless fairly obvious that this disappearing off applies to everything. Whereas your recursive argument about costs only being able to inflate is correct, they can only inflate up to a finite value at the limit due to the inflation added at each level of recursion being smaller than the last.